Questions: Suppose that on January 1 you have a balance of 4900 on a credit card whose APR is 21%, which you want to pay off in 1 year. 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 from part (b) is interest?

Suppose that on January 1 you have a balance of 4900 on a credit card whose APR is 21%, which you want to pay off in 1 year. 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 from part (b) is interest?

Transcript text: Suppose that on January 1 you have a balance of $\$ 4900$ on a credit card whose APR is $21 \%$, which you want to pay off in 1 year. 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 from part (b) is interest?

Solution

Solution Steps

Step 1: Monthly Payment Calculation

To calculate the monthly payment, we use the formula: \[PMT = \frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]}\] Substituting the given values, we get: \[PMT = \frac{4900\left(\frac{0.21}{12}\right)}{\left[1-\left(1+\frac{0.21}{12}\right)^{-12 \times 1}\right]} = 456.26\]

Step 2: Total Amount Paid Calculation

The total amount paid over the period is calculated by multiplying the monthly payment by the total number of payments: \[\text{Total Paid} = PMT \times n \times t = 456.26 \times 12 \times 1 = 5475.09\]

Step 3: Interest Paid Calculation

The total interest paid is the total amount paid minus the principal amount: \[\text{Total Interest} = \text{Total Paid} - P = 5475.09 - 4900 = 575.09\]

Step 4: Percentage of Total Payment that is Interest

The percentage of the total payment that is interest is calculated by dividing the total interest paid by the total amount paid and then multiplying by 100: \[\text{Interest Percentage} = \left(\frac{\text{Total Interest}}{\text{Total Paid}}\right) \times 100 = \left(\frac{575.09}{5475.09}\right) \times 100 = 10.5\%\]