Questions: A rare employee transited 8980 on this credit card to execute for his first job. After noticing that the interest rate for his balance was 15% compounded monthly, he stopped charging anything else on the card. If it takes 3 years using automatic payments setup at the end of each month to pay off his balance, what was the amount of each payment? a. What monthly payment must he make to pay off the account at the end of 3 years? b. How much total interest will he have paid? (Round to the nearest cent as needed.)

A rare employee transited 8980 on this credit card to execute for his first job. After noticing that the interest rate for his balance was 15% compounded monthly, he stopped charging anything else on the card. If it takes 3 years using automatic payments setup at the end of each month to pay off his balance, what was the amount of each payment? a. What monthly payment must he make to pay off the account at the end of 3 years? b. How much total interest will he have paid? (Round to the nearest cent as needed.)
Transcript text: A rare employee transited $8980 on this credit card to execute for his first job. After noticing that the interest rate for his balance was 15% compounded monthly, he stopped charging anything else on the card. If it takes 3 years using automatic payments setup at the end of each month to pay off his balance, what was the amount of each payment? a. What monthly payment must he make to pay off the account at the end of 3 years? b. How much total interest will he have paid? (Round to the nearest cent as needed.)
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Solution

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Solution Steps

Step 1: Convert the annual interest rate to a monthly rate

To find the monthly interest rate, divide the annual rate by 12.

\[r_m = \frac{r}{12} = \frac{0.15}{12} = 0.0125\]

Step 2: Calculate the total number of payments

The total number of payments is the loan term in years times 12.

\[N = n \times 12 = 3 \times 12 = 36\]

Step 3: Calculate the monthly payment

Using the formula for an amortizing loan:

\[M = P \times \frac{r_m \times (1 + r_m)^N}{(1 + r_m)^N - 1} = 8980 \times \frac{0.0125 \times (1 + 0.0125)^36}{(1 + 0.0125)^36 - 1} = 311.29\]

Step 4: Calculate the total interest paid

The total interest paid over the term of the loan is the total amount paid minus the principal.

\[Total\ Interest = (M \times N) - P = (311.29 \times 36) - 8980 = 2226.61\]

Final Answer:

The monthly payment required to pay off the loan is $311.29, and the total interest paid over the term of the loan is $2226.61.

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