If you borrow $6.65 for six years at an interest rate of 10%, how much interest will you pay?

If you borrow $6.65 for six years at an annual interest rate of 10%, you will pay $5.13 in interest if the interest is compounded annually, $5.44 if it is compounded monthly, or $3.99 if it is not compounded at all.

Expert Answers

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The exact amount of interest you pay on any loan depends on how frequently the interest is compounded. If the interest were not compounded at all, the calculation would be perfectly straightforward. 10% of $6.65 is 66.5 cents. Multiplied by 6 years, this is $3.99 in interest.

In practice, however, this never happens, because the interest is compounded at least annually. The interest for the first year would therefore be 66.5 cents (probably rounded up to 67, to give an amount in whole cents). This then means that the interest for the second year would be 10% of $7.32. Again, rounding off this sum would give 73 cents interest for the second year, meaning that the interest for the third year would be 10% of $8.05. This annual compounding of interest would give a total of $5.13 over six years.

Alternatively, if the interest were compounded once every six months, the total sum would be $5.29 over six years. Compounded monthly, it would be $5.44. Interest on loans is seldom compounded more frequently than this, but it would not make much difference if it were. Even compounding the interest daily only increases the total to $5.47. Extending the term, however, makes a much greater difference. Even adding a year increases the interest to $6.31 (compounded annually).

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