you have a $5841 credit card debt, and you plan to pay it off through monthly payments of $71. if you are being charged 14% interest per year, how long will it take you to repay your debt?
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.