# James owes $6,927 on a credit card with a 19.5% interest rate. What is the monthly payment he should make to pay off this debt in 12 months, assuming he does not charge any more purchases with the card?

a-$1531.34

b- $577.25

c-$124.82

d- $640.02

My answer is D

## correct

## thank you

## To determine the monthly payment James should make to pay off his credit card debt in 12 months, we can use the formula for the monthly payment on a loan, which is given by:

\[M = \frac{P \times r \times (1+r)^n}{(1+r)^n - 1}\]

where:

- M is the monthly payment

- P is the principal amount (the amount James owes)

- r is the monthly interest rate

- n is the number of months

Let's calculate it step-by-step:

First, let's convert the annual interest rate to a monthly interest rate. We divide the annual interest rate by 12:

\[r = \frac{19.5}{100 \times 12} = 0.01625\]

Next, substitute the given values into the formula:

\[M = \frac{6927 \times 0.01625 \times (1+0.01625)^{12}}{(1+0.01625)^{12} - 1}\]

Calculate the numerator:

\[Numerator = 6927 \times 0.01625 \times (1+0.01625)^{12} \approx 1303.93\]

Calculate the denominator:

\[(1+0.01625)^{12} - 1 \approx 0.2771\]

Finally, divide the numerator by the denominator to find the monthly payment:

\[M = \frac{1303.93}{0.2771} \approx 4703.39\]

Based on the calculations, the monthly payment James should make to pay off his credit card debt in 12 months is approximately $4703.39, which is not one of the given options.

So, it seems there might be an error in the options provided.

## To calculate the monthly payment James should make to pay off his debt in 12 months, we can use the formula for monthly payment on a loan or credit card balance. The formula is:

Monthly Payment = (Principal + (Principal * Interest Rate)) / Number of Months

Given:

Principal (Amount owed) = $6,927

Interest Rate = 19.5% per year

Number of Months = 12

Let's calculate the monthly payment using the formula:

Interest Rate per Month = Interest Rate / 12 months

= 19.5% / 12

= 0.0195 / 12

= 0.001625

Monthly Payment = ($6,927 + ($6,927 * 0.001625)) / 12

= ($6,927 + $11.26) / 12

= $6,938.26 / 12

= $578.19

The monthly payment to pay off the debt in 12 months is approximately $578.19.

Among the given answer options:

a- $1531.34

b- $577.25

c- $124.82

d- $640.02

Option D- $640.02 is closest to our calculated value of $578.19, but it is not an exact match. Therefore, your answer seems incorrect.