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YOU CAN THINK of the interested charged by a loan as the mirror opposite of the investment gains on your savings. If you borrow $1,000 and the interest rate is 12% a year, you can calculate the simple interest cost in the same way you would calculate investment gains:
$1,000 x 0.12 = $120 in interest expense
That means that your loan balance after one year would be:
$1,000 x 1.12 = $1,120
Just as investment gains compound over time, so too can interest costs. Suppose you borrowed $1,000 for five years, and you didn’t pay any of the interest or repay any of the sum originally borrowed. Your loan balance after five years would be:
$1,000 x 1.12 x 1.12 x 1.12 x 1.12 x 1.12 = $1,762
To make it easier for borrowers to compare loans, lenders are required to disclose the annual percentage rate, or APR, that they charge. This standardized loan rate takes into account both the interest charged and any fees involved.
Next: Amortizing Loans
Previous: Gordon Equation
In your example you assumed an annual compounding period without clearly stating so. Not addressing the compounding period can result in significant error. If, for example, your $1000 loan compounded monthly instead of annually as you assumed the final balance would be $1817.
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