Understanding APR - can it be calculated as a dollar amount

Question

If the APR (as used in the US Truth in Lending Act) is considered "the cost of your credit as a yearly rate," can an APR be converted to a dollar amount? For example 10% simple interest per year on a $\$100$ loan would be $\$10$ per year (right? I'm not a math whiz). So if a $\$100$ loan has an APR of 10%, would that mean 10% of the amount financed? If that was correct, wouldn't the annual figure X the number of years in the loan = the total finance charge? I've tested this using a sample TILA disclosure but it doesn't seem to work, so I'm wondering what I've got wrong. (I understand the general idea of the APR, finance charges, and amount financed).

Answer 1

Actually, it makes no sense to express APR as anything but a percentage. The reason is that APR is the effective interest rate you are actually paying due to compound interest. It is an artifact of the computation involved in compound interest and nothing else. It does not cost any additional money,; what costs money is compound interest.

For example, consider a loan having an interest rate $r$ to be paid in $12$ monthly installments per year. The APR is then

$$\left ( 1+\frac{r}{12}\right )^{12} -1$$

Note that, for sufficiently small $r$, the APR is roughly the interest rate. In general, however, this is not the case.