To calculate the monthly payment required to pay off a credit card balance, we can use the formula for an amortizing loan:
\[ M = \frac{P \times r(1 + r)^n}{(1 + r)^n - 1} \]
Where:
- \( M \) is the monthly payment
- \( P \) is the principal (initial balance)
- \( r \) is the monthly interest rate (annual interest rate divided by 12)
- \( n \) is the number of payments (months)
In this case:
- \( P = 1500 \)
- Annual interest rate = 21%, so the monthly interest rate \( r = \frac{21%}{12} = \frac{0.21}{12} = 0.0175 \)
- Length of payment period = 5 years, so \( n = 5 \times 12 = 60 \)
Substituting in the values:
\[ M = \frac{1500 \times 0.0175(1 + 0.0175)^{60}}{(1 + 0.0175)^{60} - 1} \]
Calculating \( (1 + 0.0175)^{60} \):
\[ (1 + 0.0175)^{60} \approx 2.89828 \]
Now we can substitute this back into the formula for \( M \):
\[ M = \frac{1500 \times 0.0175 \times 2.89828}{2.89828 - 1} \]
Calculating the numerator:
\[ 1500 \times 0.0175 \times 2.89828 \approx 76.0542 \]
Calculating the denominator:
\[ 2.89828 - 1 \approx 1.89828 \]
Now calculate \( M \):
\[ M \approx \frac{76.0542}{1.89828} \approx 40.0 \]
Rounding to the nearest dollar gives:
\[ M \approx 40 \]
None of the provided options exactly match, but since we have calculated approximately $40 and the nearest options are $41 and $62, we might want to double-check or use a different method.
To double-check, we can use a financial calculator or spreadsheet software to verify. A clearer computation might reflect closer to $41 per month, which is the only option near our calculated payment.
So the answer will be approximately:
- $41 (closest available option).
1 answer