Chapter 4 Section D
Suppose that on January 1 you have a balance of $\mathrm{\$}3000$ on a credit card whose APR is $12\mathrm{\%}$, 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 $\mathrm{\$}$
(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 ：$\boxed{{\displaystyle 99.64}}$ is the final answer.