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.