Copyright 1987 by Michael A Brochstein
(minor revisions done in 1998)
All rights reserved.
This manual describes F.A.T. (Financial Analysts Toolchest). F.A.T. is a package of tools (a.k.a. utilities) that assist in the financial analysis and planning of investments, loans, depreciation strategies, retirement, and other financial matters.
Effort has been made to make this manual and software package easily usable by financial laypeople. People trained in financial analysis or planning may only have to skim the introductory sections while laypeople are strongly encouraged to read them carefully before using F.A.T. An introductory textbook in accounting is recommended for anyone wishing a greater understanding of the subject matter.
The author wishes to express his appreciation to Jay Fridkis and Sam Saal for their assistance in the development of this product.
General Usage of F.A.T. ToolsAll of the tools in this package have a standardized user interface.
In order to see how a tool named "toolname" is used, enter the name of the individual tool in response to the system prompt (indicated in the example by a "$", your computer prompt may be C> or A>,...);
$toolname
Usage: toolname p
toolname v
toolname <monthly income> <monthly expenses>
toolname <monthly income> <monthly expenses> <checking
balance> <savings account balance>
In response to entering just the name of the tool, the tool gives you a "synopsis" of how to use it. According to the example above there are four ways to use this command. Starting with the third option mentioned, you would enter in response to the system prompt the toolname followed by your monthly income and your monthly expenses. If my monthly income was $25. and my monthly expenses were $23. I would enter the following;
$toolname 25 23
If I wanted to use the tool with the fourth option shown above I would have to mention four items on the "command line"; monthly income, monthly expenses, checking balance, and savings account balance. If my checking account balance was $450. and my savings account balance was $2500. I would enter the following;
$toolname 25 23 450 2500
You must enter the numbers in the order mentioned by the synopsis above. The tool can not tell if you mixed up the order since it does not have intuition into what the numbers (monthly income, etc.) should be. Using methods three and four requires you to enter either two or four "arguments" after the toolname. You can not enter any other number of arguments.
The tool mentioned above responds differently depending on the option chosen. Method three asks for two arguments while method four asks for four. The reason why there may be different ways to invoke the tool (different number of arguments) is because the same tool will do different things according as to how it is used. The later pages in this manual will explain the function of each tool in detail.
The first method mentioned above of invoking the tool asks you only to enter a "p" after the tool's name. This "p" stands for "prompt". When the tool is used in this manner it will prompt you "interactively" with questions. Your responses will provide the program with the same information as you could have put on the command line as shown above in the examples using methods three and four. Since there are two different amounts of arguments that the tool may request, enter a "carriage return" (the "Enter" key) in response to questions that ask for information not required by the particular option to use the tool. The following is an example of using the tool with the fourth method and the "p" command:
$toolname p
Enter your monthly income <$>............. 25
Enter your monthly expenses <$>........... 23
Enter your checking account balance <$>... 450
Enter your savings account balance <$>.... 2500
Below is an example of how to use the tool with the third method;
$toolname p
Enter your monthly income <$>............. 25
Enter your monthly expenses <$>........... 23
Enter your checking account balance <$>...
Enter your savings account balance <$>....
Notice that I did not enter any amounts in response to the third and fourth questions, but entered a "carriage return" only.
The second method of the using the tool is to enter a "v" after the tool's name. This will provide you with the version number of the tool, its author, and a copyright notice. Use this information when contacting the author to notify him of a comment, suggestion, or bug in the tool. Below is an example of the use of this second method;
$toolname v
toolname: Version 0.01
Copyright 1987 by Michael Brochstein
All rights reserved.
Compound Interest and Future Value
Future value is a method of calculating how much you would have at some future time if you invested a certain amount once or the same amount at regular intervals.
If you invested X dollars today and received 12 % compounded interest annually for 8 years, the tool "compound" will tell you how much you will have at the end of 8 years.
Compounding interest annually means that interest is calculated and added to your account one time a year. Monthly compounding is where interest is calculated twelve times a year. The amount of interest that is added each month is the annual interest (12%) divided by the number of months (12) or 1 % (12 % annual interest divided by 12 months). If there was daily compounding (365 times a year), the amount of interest added daily would be the annual interest (12 %) divided by the number of days in the year (365) or 0.032876 % (12 % annual interest divided by 365 days). The tool "compound" gives you the option of stating the number of compounding periods per year (the default is 1 = annually).
The tool "fv" is similar to "compound" except that it works in terms of asking for interest per compounding period and the number of periods that the investment will run for. For daily compounding in the above example you would have to use the daily interest (0.03876) and the number of days (8 years times 365 days = 2920).
Future Value of an Ordinary Annuity
An "ordinary annuity" is where equal deposits are made at equal time intervals. An example is where you make a deposit of a dollar at the beginning of each year for five years and the investment earns 2% annually (annual compounding). At the beginning of the fifth year right after you make the fifth deposit, you will have $5.20. The tool "fvoa" figures the value at this point which is referred to as the future value of an ordinary annuity.
Future Value of an Annuity Due
An "annuity due" is similar to an ordinary annuity except that in this case the last deposit is not made. In the example given in the section above, "Future Value of an Ordinary Annuity", the last deposit of one dollar is not made which then tells us that at the beginning of the fifth year you would have $4.20. The tool "fvad" figures the value at this point which is referred to as the future value of an annuity due.
Compound Interest and Present Value
Suppose someone offered to give you $100. in ten years if you gave him $40. today. Would you take the money ?
Being promised to get paid $100. in ten years is not the same as having it in your pocket today. If you had a $100. today you could invest it to earn interest and then have more than $100. in ten years. If the interest that your investment earns is 10 % annually, then in ten years you would have $259.37 assuming you did not touch either the principal (the amount you invested or the interest earned during the ten years). The use of the tool "compound" will tell you this. The tool calculates the amount of interest an investment will earn given that you make a one time investment and let the interest "compound", (i.e. letting the interest itself earn interest). Another tool, "comptbl", will tell you the same information as "compound" but will also print a table showing each years interest earned and how much your investment will have grown in that time.
Now if $100. today is worth $259.37 in ten years (at 10% interest), how much do you need today to invest so that in ten years you will have $100. ? You would need $38.55 today. This concept of how much money in your hand today (presently) would be needed in order to have a certain amount of money in the future is called "present value". The tool "pv" figures present value.
From the analysis above we find that $100. in ten years is equivalent to $38.55 today, if you can earn 10% interest. Under these conditions I wouldn't think that the person's offer was very generous since all you would need to have $100. in ten years is $38.55 today. An alternative analysis using the "fv" tool shows that $40. invested at 10% is worth $103.75, or more than the $100 promised.
Present Value of an Ordinary Annuity
An ordinary annuity can be defined as a set of withdrawls of the same amount made at equal intervals from an investment so that even with the amount not withdrawn earning interest (until it is taken out), at the end of this set of withdrawls the balance of the investment (principal) is zero. With an ordinary annuity it is assumed that withdrawls are made at the end of each time period. At the end of the last time interval when the last withdrawl is made, the annuity balance is zero.
An example of the use of this concept are calculations used for retirement planning. If you you will need to spend one dollar per year after retirement age for four years with the dollar withdrawn at the end of each year and your investment will earn 2 % annually (annual compounding) then at the beginning of the first year you will need to invest $3.81. This amount is called the present value of an ordinary annuity. The tool "pvoa" does the calculation of this amount.
Present Value of an Annuity Due
An annuity due is similar to an ordinary annuity talked about in the section above "Present Value of an Ordinary Annuity". However the present value of annuity due refers to the amount needed on deposit at the end of the first period that is just before the first withdrawl is made for the annuity.
In the example used in the section "Present Value of an Ordinary Annuity", $3.88 is needed in the investment account just before the first withdrawl of one dollar is made. The tool "pvad" figures the amount needed on deposit at the end of the first period just prior to withdrawl.
An IRA type investment is an investment where the (usually) same amount of money (currently up to $2000.) is made each year for a number of years. There are a few tools in F.A.T. to calculate the future amount that an IRA type investment will yield. The tool "ira" will tell how much you will have after investing the same amount for a number of years at a certain interest rate. "ira2" does the same except it takes into account an opening balance (maybe a rollover). "iratbl" does the same as "ira" except that it prints out a table showing how much you would have each year instead of just the total at the end of the period. "ira2tbl" does the same as "iratbl" except it takes into account an opening balance. All four tools mentioned above give you the option of specifying the number of compounding periods per year for your investment. The larger the number of compounding periods per year, the faster your principal will grow.
An amortization loan (also known as a self-amortizing loan) is one which is structured so that the periodic payments are equal even though the portions of each payment that goes for interest and principal repayment vary each period.
If you take out a mortgage of $100,000. for 30 years at 12% annual interest and make equal monthly payments then at the end of the first month you will owe interest on $100,000. outstanding for one month. At 12 % annual interest this works out to an interest rate of 1% per month. This means that after one month you will owe $1,000 in interest. If this was the total monthly loan payment then at the end of the second month you would owe another months interest on the $100,000 principal which again is $1000. At this rate you will need to pay off the loan forever since you will never be decreasing the principal amount ($100,000.) at all.
A amortization loan is structured so that in the first month you will pay this interest payment of $1000. plus a little more which will go towards decreasing the loan principal. Lets say $1028.61 was paid instead of just $1000. In this case $1000. goes towards the interest due on the principal of $100,000. and $28.61 goes towards decreasing the principal. At the end of the first month the new principle loan balance will be $99,971.39.
Now at the end of the second month our same payment of $1028.61 will be split up differently. Since the principal is now only $99,971.39 we only owe $999.71 in interest payments. This leaves $28.90 as the principal part of the monthly payment. At the end of the second month $99,971.39 - $28.90 or $99,942.49 of principle is owed. If these payments are kept up for the full 360 months (30 years) then after the last monthly payment the loan principal will have been decreased to zero.
The tool "amort" will tell you how much is needed as a monthly payment in order to pay off the principal loan in the required amount of
time at an interest rate stated. It will also tell you how much interest you have paid over the course of the loan (useful for tax planning).
A growing trend today is the use of what is called "principal pre-payments". This is the practice of sending a sum in addition to your monthly loan payment that is used solely towards repayment of the principal amount. If an additional $25. is sent each month as a principal pre-payment then the amount would go towards diminishing the principal faster. This means that the loan would be paid off faster and less interest paid since the loan period was shortened by these payments. If $25. extra was sent each month as a principal pre-payment, then the loan would be paid off in 300 months as opposed to 360 months. This would have save $54,946.60 in interest payments since the loan was held for 60 fewer months. The tool "amort" will also let you specify a principal pre-payment.
The tool "amortbl" is similar to "amort" except that it prints out a table showing each months progress towards paying off the loan.
A bond is a financial debt instrument where one entity loans another money in return for interest payments during the term of the loan and the return of the principal at the end of the loan period. The bond note represents the owing of these interest payments and the return of the principal when the life of the loan is over.
Bonds are sold initially to the public by corporations and governmental agencies and can subsequently be resold by the public in what is called the secondary market.
There are many different types of bonds. The description below is for a basic type of bond. The amount of money that is returned to you at the end of the life of the bond is called the maturity value (also called the par or face value). The interest rate based upon the bonds par value is called the coupon rate. Suppose a bond is issued with a $100. par value and stated annual interest rate of 8%. This means that the bond issuer would pay the bond holder $8. in interest each year. If the interest rate in the market place was 12% then the public would not buy the bond since the bonds "yield" was below the market rate. In order to sell the bond it would have to be priced at $66.67. Why is that ? Since 12 % of $66.67 is $8. At this price the bond will also yield the same interest as the interest rate in the market.
The bond issuer would pay $8. per year for ten years and then at the end of the tenth year return the par value to the bond holder. (The total of all payments would equal $8. per year times ten years plus $100. for a total of $180. Bonds pay interest typically twice a year although this practice varies.) The total yield on the bond is based upon how much we earn from the bond (total interest payments plus par value minus purchase price) divided by the length of the investment. If I paid $100. for this bond then I would get a yield of 8 %. If I had paid $50. for the bond then my yield would be 16 %. If the market interest rate was 16 % then $50. would be the most I would want to pay for this bond.
Another way to look at a bond is to use the "present value" techniques described in the other sections above. Evaluating the payout of interest payments is equivalent to calculating the present value of an ordinary annuity. Evaluating the payout of the par value at the end of the bond term is equivalent to calculating the present value of a single payment made at some future time. We need to know the market's interest rate for present value analysis in order to see what the payouts are worth today under current market conditions. Remember the stated interest rate (or coupon rate) of the bond is the yield based only upon the par value of the bond and not upon the purchase price of the bond.
Assume that the bond above is offered for sale at $75. when the current market interest rate for similar bonds is 11%. Is the bond priced "right"? Would you be making a smart investment by purchasing this bond instead of another? Using present value calculations we find that the present value of the bond to be $82.07. Then this bond is an attractive investment since it should cost $82.07 today to purchase an equivalent bond and you need only $75. to purchase this bond.
The tool "bond" does all the calculations mentioned in this section and should help guide you in your purchase of a bond. Remember that interest rates do change and that this tool cannot take that into account (no crystal ball here !). Changing interest rates can make a bond that is attractive today into one that is a "dog" under conditions of different interest rates.
With Social Security alone not providing an adequate source of income on which to retire, many people are planning their own investments to use during their retirement years. In order to make plans we need to calculate how much we will require each year after retirement to live the way we want to. We also need to estimate how many years we expect to live. (We will assume that there is no inflation or that interest rates will reflect the inflation rate so we can assume our investments will earn a higher amount of interest if inflation rises.)
Let us say you need $50,000 a year from your investments and expect to live 35 years after your retirement date. You also need to know how many years there are until retirement day. Assume that you intend to retire in 30 years. The tool "pvoa" will calculate how much you will need at retirement if you assume that the interest rates on your investments will be earning 10 % annually (annual compounding). "Pvoa" tells us that we need $482,207.95 on our day of retirement.
You now have to figure how much to invest today so that you will have this amount at retirement. The tool "pv" tells us that if you invest $27,634.64 today you will have the needed amount on retirement day. Since most people will not have this amount to commit to this purpose today, they will usually invest a smaller amount each year that will build until retirement into the needed amount. The tool "fvoa" tells us that if we invest $1000. each year for 30 years at 10 % annual interest we will have $164,494.02 on retirement day. We need $482,207.95 on retirement day (or $164,494.02 x 2.93146). In other words we would have to invest $2931.46 per year to get the required amount for retirement.
An easier way to perform this set of calculations is to use the tool "retire" which does all the calculations necessary by just knowing the number of years to retirement, number of years in retirement, the annual interest rate, and the amount you want to receive in payments each year. The purpose of the long winded discussion above was to explain how "retire" works and to guide you if your retirement planning investment is not as simple as the situation assumed by "retire".
What has been left out of these calculations? We have left out Social Security payments, taxes on any of your investments (usually not taken directly from the investments anyway), the knowledge of what interest rates will actually be compared to inflation, taxes on payouts from the investment if it was tax exempt during its pre-retirement life, and the knowledge of how long you will live. The last bit of knowledge could be a problem if you calculate too short a time. In the above example if you lived longer than 35 years past retirement you would not have any money left in your investment and hence no income from it after the first 35 years of retirement.
There are many other factors to consider when planning for financial security during retirement. I have only touched here on a few. Consult a professional financial planner for more information. A full discussion on other factors is beyond the scope of this publication.
There are numerous methods for calculating the depreciation to be taken each year on an asset. The most commonly used method is called "Straight-line Depreciation". This is where the salvage value of the asset is subtracted from the cost of the asset and the remaining value is divided by the number of years that the asset is expected to be useful for. For example, a machine bought for $10000. with a salvage value of $2000. and a life of 5 years would indicate a yearly depreciation expense of $1400. ((10000. - 2000.) / 5).
For certain assets it is appropriate to take depreciation at an accelerated rate, that is more depreciation expense in the earlier years of the assets life. The two most common methods of figuring accelerated depreciation are the "Double-Declining Balance" and "Sum-of-Years-Digits" methods.
In the double-declining balance method, depreciation is taken at twice the rate of straight-line depreciation. If in the above example 20% of the assets value was taken every year. With this method 40% of the "remaining" value is taken every year. Whereas in straight-line depreciation the same amount is taken every year, here 40% of the remaining value (after subtracting the salvage value as in straight-line depreciation) is taken every year. The above example would yield depreciation expenses of $4000., 2400, 1440., and 160. with no depreciation taken in the fifth year since the value of the asset minus salvage value (10000. - 2000. = 8000.) would be exceeded otherwise.
In the "Sum-of-years-digits" (SYD) method, the number of years in the life of the asset are added up (five years in the above example = 1 + 2 + 3 + 4 + 5 = 15) and this number is used as the denominator. For the numerator the years are used in reverse order. These fractions are multiplied by the value of the asset minus its salvage value ($8000.). In the first year 5/15 * 8000. or $2667.67 is taken as the depreciation expense. In the second year 4/15 * 8000. or 2133.33 is taken.
The tool "deprec" does all of the above calculations given the assets cost, salvage value, and life. It prints out a table of depreciation expenses over the life of the asset.
There are a number of tools in this package to help you figure out the terms of a loan or investment that would fit your situation. The tools can also be used to analyze a loan or investment where you do not have all the information generally required.
If you know how much interest you will be paid in a period (say per year) for an investment and how much you are starting with, you may wish to know when the investment will grow to a certain amount. Assume you invest $1000. in an investment yielding 10% per year; how many years will it take until your investment grows to $10000. ? The tool "cterm" will tell you that it would take 24.16 years (or periods in the terminology of "cterm").
You may know how much you can afford a month for loan payments on something you want to buy. You may also know what the prevailing loan rates are and how long you wish to pay out this loan over. However, you may not know how much you can get a loan for given this information. Say you are willing to make payments of $200. a month for 60 months and the prevailing loan rate is 10%. The tool "loanamt" tells you given this information that you can afford a loan of $9413.07.
Another situation might be that you know how much you can afford each month in payments, how much the item you want costs, and the loan rate. What you need to know is given these constraints, how long it would take to pay off the loan. Lets say that a car you want to buy costs $25000., you can afford payments of $400. a month, and the car loan rates are 11%. Using the tool "loanlen" we find that it will take 93.24 months to pay off the car (it better be a reliable car).
A twist on the problems of the present and future value could be a situation where you know how much you will put in an investment at its beginning and how much it will equal in a certain number of periods (years maybe). What you need to know is what its periodic (say yearly) interest rate is so that you can compare this investment to another. For example if you know that an investment of $1000. today will accrue interest so that in 10 years it will equal $4000. the tool "rate" will tell you that the yearly interest rate is 14.87% (not bad !).
Many times we are told that a sum of money is due in a certain number of days (a note or bill in 90 or 120 days etc.). Instead of counting this out on a calendar day by day or adding months and then fractions of a month together the tool "dateplus" will tell you that date on a given number of days from today. Be sure that today's date is set correctly on your computer system before using this tool.
Tool Reference ManualThe following pages contain reference pages for the various tools in the F.A.T.
Each Reference Page is divided into a number of sections some of which may not be present for some tools. The sections and a brief description of each is given below;
NAME - The name of the tool and a very brief description.
SYNOPSIS - Summarizes the use of the tool.
DESCRIPTION - Describes the tool.
EXAMPLES - Gives examples of usage of the tool.
SEE ALSO - Names other tools and places to look.
DIAGNOSTICS - Discusses diagnostic messages generated by the tool.
WARNINGS - Points out things to be aware of.
BUGS - Lists any known bugs and known limitations of the tool.
top of pageNAME
amort - amortization loan
SYNOPSIS
amort p
amort v
amort <principal> <interest> <length of loan
(months)>
amort <principal> <interest> <length of loan
(months)> <prepayment>
DESCRIPTION
Amort will calculate the monthly payment and total interest paid over the course of a loan. An optional input is a monthly "principal pre-payment" which changes to output somewhat.
EXAMPLE(S)
A loan of $100000. at 11% annual interest for 30 years (360 months);
$amort 100000 11 360
-Monthly payment.......$ 95.23
-Total interest paid...$ 24283.64
A loan of $100000. at 11 % annual interest for 30 years (360 months) with a $25. monthly principal pre-payment;
$amort 100000 11 360 25
-Regular monthly payment........$ 952.32
-Monthly principal pre-payment..$ 25.00
-Total interest paid............$ 197708.77
-Length of loan <months>......... 305
SEE ALSO
amortbl
top of pageNAME
amortbl - amortization loan payment schedule
SYNOPSIS
amortbl p
amortbl v
amortbl <principal> <interest> <length of loan (months)>
amortbl <principal> <interest> <length of loan (months)>
<prepayment>
DESCRIPTION
Amortbl generates a payment schedule for an amortization loan. An optional input is a monthly "principal pre-payment".
EXAMPLE(S)
A loan of $100000. at 13 % annual interest for 30 years (360 months);
$amortbl 100000 13 360
Monthly payment.......$ 1106.20
Total interest paid...$ 298231.83
Month Principal Paid Interest Paid Remaining loan
----- -------------- ------------- --------------
1 22.87
1083.33
99977.13
2 23.11
1083.09
99954.02
3 23.36
1082.84
99930.66
.
.
358 1071.01
35.19
2176.96
359 1082.62
23.58
1094.34
360 1094.34
11.86
0.00
-------------- -------------
100000.00
298231.83
A loan for $100000. at 13% annual interest for 360 months with a monthly principal pre-payment of $25.
$amortbl 100000 13 360 25
Regular monthly payment........$ 1106.20
Monthly principal pre-payment..$ 25.00
Month Principal Paid Interest Paid Prepayment Remaining loan
----- -------------- ------------- ---------- --------------
1 22.87
1083.33
25.00 99952.13
2 23.38
1082.81
25.00 99903.75
3 23.91
1082.29
25.00 99854.84
.
.
292 1075.98
30.22
25.00 1688.55
293 1087.91
18.29
25.00 575.64
294 575.64
6.24
0.00
0.00
-------------- -------------
100000.00
232023.34
SEE ALSO
amort
NAME
bond - bond investment analyzer
SYNOPSIS
bond p
bond v
bond <par value> <stated interest rate> <life of bond-years> <bond
price> <market interest rate> <number of interest payments per year>
DESCRIPTION
Bond figures the earnings to the bondholder over the life of the bond and also analyses the bond using time value of money concepts in light of the prevailing interest rate in the market.
EXAMPLE(S)
A bond with a par value of $100., stated interest rate of 8% annually, being held for 10 years, bought for $95., with a prevailing interest rate in the market of 10% annually, and with the bond paying its interest payments twice a year.
$bond 100 8 10 95 10 2
Total interest payments
over life of bond................. 80.00
Difference between par value
and purchase price................ 5.00
-------------
Net return to bondholder: 85.00
Average return per year........... 8.50
Approximate annual yield.......... 8.95 %
- Using present value analysis techniques;
Present value of Par value of bond.... 37.69
Present value of the annuity of
the interest payments................. 49.85
-------------
TOTAL PRESENT VALUE OF BOND: 87.54
SEE ALSO
pv, pvoa
NAME
compound - compound interest
SYNOPSIS
compound p
compound v
compound <initial investment> <interest rate> <length of investment
(years)>
compound <initial investment> <interest rate> <length of investment
(years)> <compounding periods per year>
DESCRIPTION
Calculate how much an investment will accrue to given a certain initial investment, annual interest rate, length of investment in years, and the number of compounding periods per year.
EXAMPLE(S)
An investment of $1000. at 11% annual interest for 25 years.
$compound 1000. 11 25
Total interest paid...... 12585.46
Ending balance........... 13585.46
An investment similar to above except with 12 compounding periods per year.
$compound 1000. 11 25 12
Total interest paid...... 14447.89
Ending balance........... 15447.89
SEE ALSO
comptbl
DIAGNOSTICS
Compound requires at least one compounding period a year and will use one compounding period a year if the entered value is less than 1.
WARNINGS
Default number of compounding periods annually is one.
NAME
comptbl - compound interest schedule
SYNOPSIS
comptbl p
comptbl v
comptbl <initial investment> <interest rate> <length of investment
(years)>
comptbl <initial investment> <interest rate> <length of investment
(years)> <compounding periods per year>
DESCRIPTION
Generate a table showing how an initial investment at a certain annual interest rate for a set period of years will do. An optional field lets the user set the number of compounding periods per year.
EXAMPLE(S)
An investment of $1000. at 11% annually for 5 year;
$comptbl 1000 11 5
Year Interest Paid Year End Balance
---- ------------- ----------------
0 0.00
1000.00
1 110.00
1110.00
2 122.10
1232.10
3 135.53
1367.63
4 150.44
1518.07
5 166.99
1685.06
---- ------------- ----------------
TOTAL: 685.06 1685.06
An investment of similar to above except with 12 compounding periods per year.
$comptbl 1000 11 5 12
Year Interest Paid Year End Balance
---- ------------- ----------------
0 0.00
1000.00
1 115.72
1115.72
2 129.11
1244.83
3 144.05
1388.88
4 160.72
1549.60
5 179.32
1728.92
---- ------------- ----------------
TOTAL: 728.92 1728.92
SEE ALSO
compound
DIAGNOSTICS
User input of less than 1 compounding period per year results in usage of 1 compounding period per year by comptbl.
WARNINGS
Default number of compounding periods annually is 1.
NAME
cterm - find compounding term
SYNOPSIS
cterm p
cterm v
cterm <present value> <future value> <interest per compounding period>
DESCRIPTION
Cterm finds the length of a investment necessary for the investment to grow from a present value to a future value at a given interest rate per compounding period. The answer given is in terms of periods.
EXAMPLE(S)
To find how long it would take $1000. to increase to $10000. at an annual interest rate of 7.5%.
$cterm 1000 10000 7.5
It will take 31.84 periods.
SEE ALSO
rate
NAME
dateplus - todays date plus some days
SYNOPSIS
dateplus p
dateplus v
dateplus <number of days to add to today>
DESCRIPTION
Dateplus tells the user the date it will be in a given number of days from today.
EXAMPLE(S)
If today is 12/14/86 and I want to know what the date will be in 125 days;
$dateplus 125
Sunday December 14 1986 plus 125 days is Saturday April 18 1987.
DIAGNOSTICS
Dateplus will tell the user when it has asked for a date beyond what it can see into the future.
WARNINGS
Dateplus can only "see" until January 19, 2038.
BUGS
In addition to only seeing until 1/19/2038, dateplus CAN see backwards until about the year 1900 if you enter a minus number as input to dateplus.
NAME
deprec - depreciation method analyzer
SYNOPSIS
deprec p
deprec v
deprec <cost> <salvage value> <life (years)>
DESCRIPTION
Deprec generates a table showing yearly depreciation expenses for an asset over its life. It shows the expenses for the "straight- line", "double-declining balance" and "sum-of-years-digits" methods.
EXAMPLE(S)
For an asset with a cost of $10000., a salvage value of $2000., and a life of 5 years;
$deprec 10000 2000 5
Double-Declining Sum-of-the-years
Year Straight Line Balance
Digits
---- ------------- ---------------- ----------------
1 1600.00
4000.00
2666.67
2 1600.00
2400.00
2133.33
3 1600.00
1440.00
1600.00
4 1600.00
160.00
1066.67
5 1600.00
0.00
533.33
---- ------------- ---------------- ----------------
TOTAL: 8000.00 8000.00
8000.00
NAME
fv - future value
SYNOPSIS
fv p
fv v
fv <principal> <interest rate per compounding period> <number of
compounding periods>
DESCRIPTION
Fv finds the future value of an investment (principal) which is invested for a number of compounding periods at a certain rate per compounding period.
EXAMPLE(S)
For an investment of $1000. which earns 12% per year (period) for a length of 15 years (compounding periods);
$fv 1000 12 15
Future value........... 5473.57
For an investment similar to above except that interest is compounded monthly;
$fv 1000 1 180
Future value........... 5995.80
SEE ALSO
compound, comptbl
NAME
fvad - future value of an annuity due
SYNOPSIS
fvad p
fvad v
fvad <deposit amount> <interest rate per compounding period> <number of
deposits (include last deposit)>
DESCRIPTION
Fvad finds the future value of an annuity due where the same amount is deposited regularly at a certain amount of interest per compounding period for a number of periods. The last deposit is never made since this is an annuity due but is counted when entering the number of deposits as an argument to this tool.
EXAMPLE(S)
For a deposit of $2000. made every year for 20 years at the beginning of the year and the last deposit is not made. How much is there at the beginning of the 20th year ? The annual interest rate is 11%.
$fvad 2000 11 20
Future value........... 126405.66
SEE ALSO
fvoa, ira, ira2
NAME
fvoa - future value of an ordinary annuity
SYNOPSIS
fvoa p
fvoa v
fvoa <deposit amount> <interest rate per compounding period> <number of
deposits>
DESCRIPTION
Fvoa find the future value of a set of equal deposits made one to a period for a given number of periods at a given interest rate per period.
EXAMPLE(S)
Find the value of an annuity where $2000. is deposited each year for 20 years at an annual interest rate of 11%.
$fvoa 2000 11 20
Future value........... 128405.66
SEE ALSO
fvad, ira, ira2
NAME
ira - IRA investment
SYNOPSIS
ira p
ira v
ira <yearly investment> <interest rate> <length of investment (yrs)>
ira <yearly investment> <interest rate> <length of investment (yrs)>
<compounding periods per year>
DESCRIPTION
Ira will figure how much an yearly investment of equal amounts will grow into in a given amount of years at a given interest rate. Optionally the number of compounding periods per year can also be set.
EXAMPLE(S)
For an investment of $2000. per year for 35 years yielding 10% annually.
$ira 2000 10 35
Total amount invested......... 70000.00
Total interest earned......... 526253.61
Ending Balance................ 596253.61
For an investment similar to above except with monthly compounding.
$ira 2000 10 35 12
Total amount invested......... 70000.00
Total interest earned......... 597569.61
Ending Balance................ 667569.61
SEE ALSO
ira2, iratbl, ira2tbl, fvoa, retire
DIAGNOSTICS
Ira will reject investments with less than one compounding period a year, it will default to one compounding a year under these circumstances.
WARNINGS
Ira will default to one compounding period per year.
NAME
ira2 - IRA investment with an opening balance
SYNOPSIS
ira2 p
ira2 v
ira2 <yearly investment> <interest rate> <length of investment (years)>
<opening balance>
ira2 <yearly investment> <interest rate> <length of investment (years)>
<opening balance> <compounding periods per year>
DESCRIPTION
Ira2 calculates how much an investment will yield on an investment of equal amounts for a given period of years and at a given interest. An opening balance must be specified. Optionally the number of compounding periods per year can be varied.
EXAMPLE(S)
For an investment of $2000. per year for 35 years at 8 % interest with an opening balance of $5000.
$ira2 2000 8 35 5000
Opening Balance............... 5000.00
Total amount invested......... 70000.00
Total interest earned......... 371131.02
Ending Balance................ 446131.02
For an investment similar to above except with 12 compounding periods per year.
$ira2 2000 8 35 5000 12
Opening Balance............... 5000.00
Total amount invested......... 70000.00
Total interest earned......... 405545.22
Ending Balance................ 480545.22
SEE ALSO
ira, iratbl, ira2tbl, fvoa, retire
DIAGNOSTICS
Ira2 requires at least one compounding period per year and an opening balance of at least year. Diagnostic messages will tell the user if these requirements are not met and will default to a zero opening balance and one compounding period per year.
WARNINGS
Use at least one compounding period per year and an opening balance >= 0.
NAME
ira2tbl - IRA investment schedule with an opening balance
SYNOPSIS
ira2tbl p
ira2tbl v
ira2tbl <yearly investment><interest rate><length of investment (years)>
<opening balance>
ira2tbl <yearly investment><interest rate><length of investment (years)> <opening balance> <compounding periods per year>
DESCRIPTION
Ira2tbl prints a table showing the progress of an IRA type investment. The investment is of equal deposits made once a year at a given interest and for a given number of years. An opening balance must be specified and the number of compounding periods per year can be varied from the default of one.
EXAMPLE(S)
For an investment of $2000. a year at 7% interest for 35 years with an opening balance of $3500.
$ira2tbl 2000 7 35 3500
Year Amount Invested Interest Paid Year End Balance
---- --------------- ------------- ----------------
0 2000.00
0.00
5500.00
1 2000.00
385.00
5885.00
2 2000.00
551.95
8436.95
.
.
33 2000.00
18785.92 287156.22
34 2000.00
20240.94 309397.15
35 2000.00
21797.80 333194.95
---- --------------- ------------- ----------------
TOTAL: 70000.00 259694.95
333194.95
For a similar investment to above except with 12 compounding periods per year.
$ira2tbl 2000 7 35 3500 12
Year Amount Invested Interest Paid Year End Balance
---- --------------- ------------- ----------------
0 2000.00
0.00
5500.00
1 2000.00
397.60
5897.60
2 2000.00
570.92
8468.51
.
.
33 2000.00 20375.31
302230.22
34 2000.00 21992.83
326223.05
35 2000.00 23727.27
351950.32
---- --------------- ------------- ----------------
TOTAL: 70000.00 278450.32
351950.32
SEE ALSO
ira, ira2, iratbl, fvoa, retire
DIAGNOSTICS
Failure to specify an opening balance >= 0 will result in an opening balance of 0 to be used along with a diagnostic message stating this.
Specification of less than one compounding period per year will result in one compounding period per year being used in calculations and a diagnostic message stating this.
WARNINGS
Opening balance must be >= 0. If specified, compounding periods per year must be >= 1. Defaults are 0 and 1 respectively.
NAME
iratbl - IRA investment schedule
SYNOPSIS
iratbl p
iratbl v
iratbl <yearly investment> <interest rate> <length of investment (yrs)>
iratbl <yearly investment> <interest rate> <length of investment (yrs)>
<compounding periods per year>
DESCRIPTION
Iratbl will print a table showing how an investment of equal amounts made yearly for a given number of years and interest rate will do over its life. Optionally the number of compounding periods per year can be varied.
EXAMPLE(S)
For an investment of $2000. at 9 % for 35 years;
$iratbl 2000 9 35
Year Amount Invested Interest Paid Year End Balance
---- --------------- ------------- ----------------
0 2000.00
0.00
2000.00
1 2000.00
180.00 2180.00
2 2000.00
376.20 4556.20
.
.
33 2000.00
32364.06 391964.69
34 2000.00
35456.82 429421.51
35 2000.00
38827.94 470249.45
---- --------------- ------------- ----------------
TOTAL: 70000.00 400249.45
470249.45
For an investment similar to above except with 12 compounding periods per year.
$iratbl 2000 9 35 12
Year Amount Invested Interest Paid Year End Balance
---- --------------- ------------- ----------------
0 2000.00
0.00
2000.00
1 2000.00
187.61 2187.61
2 2000.00
392.83 4580.44
.
.
33 2000.00
36554.20 426229.18
34 2000.00
40170.85 468400.03
35 2000.00
44126.77 514526.79
---- --------------- ------------- ----------------
TOTAL: 70000.00 444526.79
514526.79
SEE ALSO
ira, ira2, ira2tbl, fvoa, retire
DIAGNOSTICS
Iratbl requires at least one compounding period per year and will default to one when presented with less than one.
WARNINGS
Use at least one compounding period per year.
NAME
loanamt - find amount that can be loaned
SYNOPSIS
loanamt p
loanamt v
loanamt <monthly payment> <length of loan (months)> <annual interest
rate>
DESCRIPTION
Loanamt calculates how much one can loan given a certain monthly payment, loan length, and annual loan interest rate.
EXAMPLE(S)
For a monthly payment of $325. for 48 months with a loan rate of 11% you can borrow:
$loanamt 335 48 11
Amount that can be borrowed...... 12961.63
SEE ALSO
loanlen
NAME
loanlen - find loan length
SYNOPSIS
loanlen p
loanlen v
loanlen <principal> <monthly payment> <annual interest rate>
DESCRIPTION
Loanlen calculates the length that a loan has to be given a certain principal to be paid off, a certain monthly payment, and an annual loan interest rate.
EXAMPLE(S)
For a loan of $18,000. at an 11% loan interest rate with a monthly payment of $350. How long will it take to pay off ?
$loanlen 18000 350 11
Number of monthly payments needed...... 69.87
SEE ALSO
loanamt
NAME
pv - present value in terms of months and years
SYNOPSIS
pv p
pv v
pv <future value> <interest rate (yearly)> <length of time (months)>
pv <future value> <interest rate (yearly)> <length of time (months)>
<compounding periods per year>
DESCRIPTION
Pv figures the present value of an amount of money (future value) based on the number of months into the future the money will be available, the yearly interest rate and optionally greater than the default of one compounding period per year.
EXAMPLE(S)
Having $1000. in ten years (120 months) at an annual interest rate of 9% is the same as having how much today?
$pv 1000 9 120
Present value........... 422.41
For an situation similar to above except with 12 compounding periods per year;
$pv 1000 9 120 12
Present value........... 407.94
SEE ALSO
pv2
DIAGNOSTICS
Specification of less than one compounding period per year results in a diagnostic message and a one compounding period per year being used in the calculations.
WARNINGS
If specifying the number of compounding periods per year, it must be >= 1 of the default will be 1.
NAME
pv2 - present value in terms of periods and interest per period
SYNOPSIS
pv2 p
pv2 v
pv2 <future value> <interest rate per compounding period> <number of
compounding periods>
DESCRIPTION
Pv2 calculates the present value of an amount (future value) in terms of being able to receive a certain interest rate per compounding period and a given number of compounding periods.
EXAMPLE(S)
Having $1000. in 7 years with an annual interest rate of 12% is that same as having how much today?
$pv2 1000 12 7
Present value........... 452.35
In a situation similar to above except with monthly compounding of interest.
$pv2 1000 1 84
Present value........... 433.52
SEE ALSO
pv
NAME
pvad - present value of an annuity due
SYNOPSIS
pvad p
pvad v
pvad <withdrawl amount> <interest rate per compounding period> <number of
withdrawls>
DESCRIPTION
Pvad calculates the present value of an annuity that pays a certain withdrawl amount per period while earning a certain interest rate during that time for a set number of periods. The value is taken at right before the first payment.
EXAMPLE(S)
What is the present value of an annuity right before its first payout where $1500. is paid out per month, the investment earns 18% a year, and withdrawls are made for 20 years ?
$pvad 1500 1.5 240
Present value........... 98651.50
SEE ALSO
pvoa
NAME
pvoa - present value of an ordinary annuity
SYNOPSIS
pvoa p
pvoa v
pvoa <withdrawl amount> <interest rate per compounding period> <number of
withdrawls>
DESCRIPTION
Pvoa calculates the present value of an ordinary annuity given a certain withdrawl amount per period, interest per period, and for a number of withdrawls.
EXAMPLE(S)
What is the present value needed for a annuity that will pay $1000. per month at 12% annual interest for 30 years ?
$pvoa 1000 1 360
Present value........... 97218.33
SEE ALSO
pvad
NAME
rate - find interest rate of an investment
SYNOPSIS
rate p
rate v
rate <present value> <future value> <number of periods>
DESCRIPTION
Rate calculates the interest rate (per period) of an investment given its value today (present value), its value at the end of the investment (future value), and the length of the investment (in
periods).
EXAMPLE(S)
What is the annual interest rate if it takes $1000. 5 years to grow to $2000.?
$rate 1000 2000 5
Interest rate per period...... 14.870 %
What is the monthly interest rate for the above situation?
$rate 1000 2000 60
Interest rate per period...... 1.162 %
SEE ALSO
loanamt, loanlen
NAME
retire - retirement planner
SYNOPSIS
retire p
retire v
retire <years to retirement> <annual interest rate> <years in
retirement> <amount wanted per year in retirement>
DESCRIPTION
Retire helps you plan your retirement. If you can predict how much money you will need in retirement each year to withdraw from your retirement investment as well as how long you expect to be retired for and you can predict the interest rate for your investments, retire can tell you how to get this needed money by either investing a sum each year until retirement or investing a lump sum
today.
EXAMPLE(S)
How can I in retirement, which is in 30 years, withdraw $50000. a year from my retirement investment while in retirement if I expect to need this for 35 years in retirement and the annual interest rate on my investments is 10% ?
$retire 30 10 35 50000
Amount needed on retirement day............. 482207.95
Option 1: Lump sum needed to invest today... 27634.64
Option 2: Amount to be invested yearly
until retirement..................
2931.46
SEE ALSO
pvoa, pv, fvoa
WARNINGS
Consult a professional financial planner, don't rely solely upon this tool.
BUGS
Ability of tool user to predict inflation rate, years to live in retirement,...
MAB Systems Inc. encourages users of its products to submit feedback of all sorts (suggestions, criticisms, comments, bugs,...) since it will be this feedback that will enable us to keep our products in tune with what you the user wants. This feedback is requested for both documentation (this manual) and software.
Bugs are a permanent part of the software landscape. All software in this package has been tested in numerous ways. Unfortunately it is impossible to test this software for all possible combinations of input data. Should you find a bug, incorrect answer, or similar problem please note the exact situation including inputs to the tool in question, version of the software as found by saying "toolname v", and the computer and operating system being used. Before sending or phoning in your bug report please make sure the bug is reproducible by trying the "error conditions" more than once. Please include your full name, address, and phone number so that we can reply to your bug report.
Please send all feedback to: Michael_Brochstein@MABsystems.com