Mathematics of Individual Finance
When you are repaying an amortized loan such as a mortgage and an installment loan, it is often necessary to calculate the amount of interest you have paid in a given period, for tax reasons, or the remaining balance on the loan in the event that you want to refinance it or borrow against the equity. Calculating an amortization schedule without a computer or a specialized calculator is tedious and time-consuming but is relatively straightforward. You merely calculate the interest for the first period, subtract that from the amount of the payment, and the difference is amortization which reduces the principal. A simple example will show how it is done.
| PERIOD | BEGINNING BALANCE | INTEREST AT (1O%) | AMORTIZATION PAYMENT-INTEREST |
|---|---|---|---|
| 1 | $10,000.00 | $1000.00 | $1637.97 |
| 2 | $8,362.03 | $836.20 | $1,801.67 |
| 3 | $6,560.26 | $656.03 | $1,981.94 |
| 4 | $4,578.32 | $457.83 | $2,180.14 |
| 5 | $2,398.18 | $239.81 | $2,398.15 |
In spite of rounding error, we end up within 3 cents of the correct final balance. Many calculators are programmed to give you the balance or interest as of a certain payment, saving the tedium of setting up such a table. Of course, this is an ideal job for a spreadsheet which handles repetitive processes without complaint. Another quick method of solving for the principal at the end of n periods is through the following formula:
| P | = (C/r)[1-1/(1+r)n] | |
| = ($2,637.97/.1)[1-1/(1.1)3] | ||
| = ($26,379.70)[1-1/1.331] | ||
| = ($26,379.70)[.2486852] | ||
| = $6,560.24 |

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