Questions: Consider a credit card with a balance of 8000 and an APR of 16.99%. In order to pay off the balance in 3 years, what monthly payment would you need to make? Round your answer to the nearest cent, if necessary.

Consider a credit card with a balance of 8000 and an APR of 16.99%. In order to pay off the balance in 3 years, what monthly payment would you need to make? Round your answer to the nearest cent, if necessary.

Transcript text: Consider a credit card with a balance of $\$ 8000$ and an APR of $16.99 \%$. In order to pay off the balance in 3 years, what monthly payment would you need to make? Round your answer to the nearest cent, if necessary.

Solution

Solution Steps

Step 1: Convert the APR from a percentage to a decimal

To convert the APR of 16.99% to a decimal, we divide by 100: $r = 0.17$.

Step 2: Calculate the monthly interest rate

The monthly interest rate $i$ is calculated by dividing the APR by 12: $i = 0.0142$.

Step 3: Calculate the monthly payment

Using the formula $M = \frac{B \cdot i}{1 - (1 + i)^{-12n}}$, where $B = 8000$, $i = 0.0142$, and $n = 3$, we find $M = 285.18$.

Final Answer:

The monthly payment required to pay off the balance in 3 years is $285.18.

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