Questions: Use PMT = P(r/n) / [1 - (1 + r/n)^(-nt)] to determine the regular payment amount, rounded to the nearest dollar. Your credit card has a balance of 5200 and an annual interest rate of 12%. You decide to pay off the balance over three years. If there are no further purchases charged to the card, a. How much must you pay each month? b. How much total interest will you pay? a. The monthly payments are approximately b. The total interest paid over 3 years is approximately (Round to the nearest dollar as needed.)

Use PMT = P(r/n) / [1 - (1 + r/n)^(-nt)] to determine the regular payment amount, rounded to the nearest dollar. Your credit card has a balance of 5200 and an annual interest rate of 12%. You decide to pay off the balance over three years. If there are no further purchases charged to the card, a. How much must you pay each month? b. How much total interest will you pay? a. The monthly payments are approximately b. The total interest paid over 3 years is approximately (Round to the nearest dollar as needed.)
Transcript text: Use PMT $=\frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]}$ to determine the regular payment amount, rounded to the nearest dollar. Your credit card has a balance of $\$ 5200$ and an annual interest rate of $12 \%$. You decide to pay off the balance over three years. If there are no further purchases charged to the card, a. How much must you pay each month? b. How much total interest will you pay? a. The monthly payments are approximately $\$$ $\square$ (Do not round until the final answer. Then round to the nearest dollar as needed.) b. The total interest paid over 3 years is approximately $\$$ $\square$ (Round to the nearest dollar as needed.)
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Solution

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Solution Steps

Step 1: Convert the annual interest rate from a percentage to a decimal

To convert the annual interest rate to a decimal, divide by 100: \(r = 12 / 100 = 0.12\).

Step 2: Calculate the monthly interest rate

The monthly interest rate is calculated by dividing the annual interest rate by the number of payments per year: \(\frac{r}{n} = \frac{0.12}{12} = 0.01\).

Step 3: Calculate the total number of payments

The total number of payments is the number of years times the number of payments per year: \(n \times t = 12 \times 3 = 36\).

Step 4: Use the PMT formula to calculate the monthly payment amount

Using the PMT formula: \(PMT = \frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]} = 173\).

Step 5: Calculate the total interest paid

The total interest paid over the period is the monthly payment amount times the total number of payments minus the principal amount: \((173 \times 36) - 5200 = 1028\).

Final Answer:

The monthly payment amount is $173, and the total interest paid over the period is $1028.

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