To determine how long it will take to repay the credit card debt, we can use the formula for calculating the number of periods (months) required to pay off a loan:
n = - log(1 - (r * P) / A) / log(1 + r)
Where:
n is the number of periods (months)
r is the monthly interest rate (annual interest rate divided by 12)
P is the principal balance (credit card debt)
A is the fixed monthly payment
Let's calculate it step by step:
Step 1: Convert the annual interest rate to a monthly interest rate.
The annual interest rate is 14%. To calculate the monthly interest rate, we divide it by 12:
Monthly interest rate (r) = 14% / 12 = 0.014
Step 2: Plug in the values into the formula:
n = - log(1 - (0.014 * $5841) / $71) / log(1 + 0.014)
Step 3: Calculate the numerator first:
Numerator = (0.014 * $5841) / $71 = $0.11534
Step 4: Calculate the denominator:
Denominator = log(1 + 0.014)
Step 5: Substitute back into the formula:
n = - log(1 - $0.11534) / log(1 + 0.014)
Step 6: Use a calculator to solve the equation:
n ≈ 135.42.
The result is an approximate value of 135.42 months (or 135 months and about 13 days).
Therefore, it would take approximately 135 months to repay the $5841 credit card debt with monthly payments of $71, assuming a 14% annual interest rate.