Chapter 4 Section D
Suppose that on January 1 you have a balance of $\$ 3000$ on a credit card whose APR is $12 \%$, which you want to pay off in 3 years. Assume that you make no additional charges to the card after January 1
a. Calculate your monthly payments.
b. When the card is paid off, how much will you have paid since January 1 ?
c. What percentage of your total payment (part b) is interest?
a. The monthly payment is $\$$
(Do not round until the final answer. Then round to the nearest cent as needed)
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Step 1 ：Given that the balance on the credit card is $3000, the APR is 12%, and the time to pay off is 3 years, we need to calculate the monthly payments.

Step 2 ：To do this, we use the formula for the monthly payment on a loan: \(P = \frac{r \times PV}{1 - (1 + r)^{-n}}\), where \(P\) is the monthly payment, \(r\) is the monthly interest rate (annual rate / 12), \(PV\) is the present value or principal amount, and \(n\) is the number of payments (3 years * 12 months/year).

Step 3 ：Substituting the given values into the formula, we get \(P = \frac{0.01 \times 3000}{1 - (1 + 0.01)^{-36}}\).

Step 4 ：Calculating the above expression, we find that the monthly payment is approximately $99.64.

Step 5 ：\(\boxed{99.64}\) is the final answer.