The most important factor in a marital relationship is the wise management of the family income. I strongly recommend that dating or married couples consider mastering the simple financial calculations in this document. I have transcribed the reference document verbatim to the level allowed by Mathcad. The numerical results exactly match all of the examples provided in the reference article given included at the end of the Mathcad calculations. This last method is useful when borrowing or lending and need to know the interest rate of return (ROR) being paid or collected, respectively. Henceforth, let us refer to i simply, as ROR.

1. MathCAD - Seven Common Financial Computations.xmcd
Seven Common Financial Computations
by Julio C. Banks, PE
This article assists any person in making financial decisions, such as renting Vs.
leasing. Seven common financial computations are illustrated here. The seven
procedures to be described are calculations of:
Loan Payment1.
Loan Balance2.
Future Value (FV) of a Lump-Sum (PV) Invested3.
Future Value of a Series of Regular Investments4.
Terms (or Years) of Lump-Sum Investments5.
Terms (or Years) of an Annuity or a Series of Regular Investments6.
Interest Rate or Rate of Return (ROR)7.
Monthly payments requre that k be set to 12 as k 12 payments per compoound
period.
1. Calculate a Loan Payment
To perform this calculation, you need to know the loan amount (PV), interest rate (i),
and the number of payments, N. Suppose, for example, that you were thinking about
purchasing or refinancing a home. You already know much money you want to borrow.
And you can flip through the Sunday paper to check out lender rates and terms. That's
about all you need to calculate a loan payment. The formula is
Payment
i
1 1 i( )
N
 
PV=
Example 1: PV 100 10
3
 i
12%
k
 N 30k
Answer: Payment
i
1 1 i( )
N
 
PV 1028.61
2. Calculate a Loan Balance
One can calculate an outstanding loan balance if one knows the loan payment, the
interest rate, and number of remaining payments, n. This procedure is useful when
trying to pay-off an existing loan. The formula is
Loan_Balance
1 1 i( )
N
 
i
Payment
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2. MathCAD - Seven Common Financial Computations.xmcd
Example 2: i
12%
k
 n 2k Payment 250
Answer: Loan_Balance
1 1 i( )
n
 
i
Payment 5310.85
3. Calculate the Future Value of a Lump-sum Investment
You can calculate the future value of an investment if you know the initial investment
amount, the interest rate the investment earns, and the number of years, N, the given
interest is earned. The formula is
Loan_Balance 1 i( )
N
PV
Example 3: PV 10 10
3
 i 10% N 10
Answer: Loan_Balance 1 i( )
N
PV 25937.42
4. Calculate the Future Value of a Series of Regular Investments
The future value of a series of equal investments can be calculated when the annual
(or monthly) investment amounts, the number of annual (or monthly) investments made
and the annual (or monthly) interest rate are given. The formula is
Future_Value
1 i( )
N
1
i






Payment
For example, if you currently plan to contribute $1,800 a year, k 1 , to your
Individual Retirement Account (IRA), to earn 12% annually, you could use this formula
to
estimate the account balance accumulated after 20 years.
Example 4a: Payment
1.8 10
3

k
 i
12%
k
 N 20k
Answer: Future_Value
1 i( )
N
1
i






Payment 129694.40
It should be noted that the above investment when made on a monthly basis k 12 ,
will produce a higher yield as shown in the next example below
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3. MathCAD - Seven Common Financial Computations.xmcd
Example 4b: Payment
1.8 10
3

k
150.00 i
12%
k
 N 20k
Answer: Future_Value
1 i( )
N
1
i






Payment 148388.30
Where Payment 150.00 per month
Therefore, a monthly investment of $150 (an equivalent annual investment of $1800)
yields a 14.414% increase in yield, i.e., $18693.90 additional money is realized.
5. Calculate the term of a lump-sum investment
You can calculate the term of an investment, or the years it will take for an investment
to reach a specified future value, if you know the present investment value, the future
value of the given investment, and the interest rate the investment will earn. The
formula is
Terms
ln
FV
PV






ln 1 i( )
=
Determine how long will it take a $50,000 inheritance earning 14% annual interest to
grow to $1,000,000
Example 5: PV 50 10
3
 FV 1 10
6
 i 14%
Answer: Terms
ln
FV
PV






ln 1 i( )
22.86 i.e., in 23 years the PV becomes FV
6. Calculate the Term of an Annuity or a Series of Regular Investments
If you know the regular investment amount, the future investment value, and the annual
interest rate the investments will earn, the term of an annuity (or number of years) is
calculated as follows
Example 6: PMT 5 10
3
 FV 1 10
6
 i 10%
Answer: Terms
ln 1 i
FV
PMT






ln 1 i( )
31.9
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4. MathCAD - Seven Common Financial Computations.xmcd
Therefore, it will take approximately 32 years for a $5,000 annual contribution to a 401
(k) fund to become a millionaire, if the 401 (k) fund earns 10% per year.
7. Calculate an Interest Rate, or Rate of Return (ROR)
You can calculate the interest rate an investment earns when you know the present
investment value, PV, the future investment value, FV, and the number of years (or
months) over which the interest can be earned. The procedure is illustrated by the
following example.
Suppose that you have a balance of $17,000 in your company profit-sharing, and a
financial planner has recommended that you should have $500,k in retirement savings
in 20 years. Calculate the required rate of return (i.e., interest rate earned), to meet your
your financial goal.
Example 7a: PV 17 10
3
 FV 0.5 10
6
 N 20
Answer: i
FV
PV






1
N
1 18.42% i.e., ROR is 18.42% APR (Annual
Percentage Rate)
This last method is useful when borrowing or lending and need to know the interest
rate of return (ROR) being paid or collected, respectively. Henceforth, let us refer to i
simply, as ROR.
A person is offered a 3-month peer-to-peer (personal) loan with with interest rate TBD
(To Be Determined) from given data. Notice that N = 1/3rd of a year.
Example 7b: PV 3.5 10
3
 FV 3.85 10
3
 N 0.3
Answer: ROR
FV
PV






1
N
1 37.4% i.e., ROR is 37.4% APR (Annual
Percentage Rate)
Reference
S. L. Nelson, "Perform Financial Feats with the Windows Calculator', PC/Computing,
November 1991. Pages 254-258.
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