# Math

You plan on borrowing \$14000 at 16% APR for 5 years. Use Web Loan Calculator to find the monthly payment. Find the total interest paid on this loan for the first 20 months.

Set up a spread sheet to answer. Here is an example of what it should look like. All cells in lower portion are formulas. You can use my examples numbers to test your spread sheet before you answer the questions. This is what is known as an amortization of the loan.

What is the monthly payment found on a bank web site?

\$
per month. (rounded to nearest cent)

After 20 months of payments, how much total interest has been paid for this loan? Use a spreadsheet to answer, round to nearest cent.

\$
of interest in the first 20 payments.

1. I used
http://www.calculatorweb.com/calculators/loancalc.shtml
and got a payment of \$3404.53 , but I learned nothing about the actuarial math involved.

Present value = 140000
n = 5(12) = 60
i = .16/12 = .013333...
(ridiculously high rate for current rates, time to get a new text)
Payment = p
p(1 - 1.01333..^(-60) )/.01333... = 140000
p(41.12170722..) = 140000
p = 3404.53

value of debt after 20 periods if no payment had been made:
140000(1.01333..)^20 = \$182,462.92

amount of 20 payment at that time
= 3404.53(1.01333..^20 - 1)/.01333.. = \$77,446.22
outstanding balance after 20 periods
= 182462.92 - 77446.22 = \$105,016.70

actual amount paid off = 140,000 - 105,016.70
= \$34,983.30
actual amount paid = 20(3404.53) = \$68,090.60
interest = \$68,090.60 - \$34,983.30 = \$33,107.30

The last paragraph of calculations would be totally invalid and unacceptable to an actuarial mathematician, since you cannot add up monetary values that are not in the same "time spot" on a time-line.
In your spread sheet, there might be a splitup of the monthly payments into "interest" and "repayment".
The sum of the column for "interest" for 20 lines should be 33107.30

posted by Reiny

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