Chapter P, Problem 16E

The Truth in Lending Act Many lending agencies compound interest more often than yearly, and, as we noted in Example P.2, they are required to report the annual percentage rate, or APR, in a prominent place on the loan agreement. Furthermore, they are required to calculate the APR in a specific way. If $r$ is the monthly interest rate, then APR is calculated using

$APR=12\times r$.

a. Suppose a credit card company charges a monthly interest rate of $1.9\%$. What APR must the company report?

b. The phrase annual percentage rate leads some people to believe that if you barrow $\$6000$ from a credit card company that quotes an APR of $22.8\%$, and if no payments are made, then at the end of 1 year, the interest would be calculated as $22.8\%$ simple interest on $\$6000$. How much would you owe at the end of a year if interest is calculated in this way?

c. If Interest is calculated monthly (which is common), then the actual amount you would owe in the situation of part b is given by

$6000\times {1.019}^{12}$.

What is the actual amount you would owe at the end of a year?