Chapter 4.5, Problem 6E

Reminder Round all answers to two decimal places unless otherwise indicated.

Minimum Monthly Payment Suppose you have a balance of $B$ dollars on credit card.You choose to stop charging and pay off the card, making only minimum monthly payments.If your card charges an APR of $r$, as a decimal, and requires a minimum monthly payment of $5\%$ of the balance, then the time $T$, in months, required to reduce your balance to $\$100$ is given by

$T=\frac{2-\log B}{\log \left(0.95\left(1+r/12\right)\right)}$.

Suppose your current balance is $\$8000$.

a. How long will it take to reduce your balance to $\$100$ if the APR for your card is $25\%$? Report your answer to the nearest whole month.

b. Plot the graph of $T$ versus $r$. Use a horizontal span of $0$ to $0.3$.

c. Does a larger APR mean a longer or a shorter time to reduce the balance to $\$100$?