Calculate the monthly payment for a student loan of $54,112 at a fixed APR of 5% for 12 years.
To calculate the monthly payment for a student loan, we can use the formula for the monthly payment amount on a fixed-rate loan. The formula is:
M = P [i(1 + i)^n] / [(1 + i)^n - 1]
Where:
M = monthly payment
P = loan amount (principal)
i = monthly interest rate (annual interest rate divided by 12)
n = number of monthly payments (years multiplied by 12)
First, let's calculate the monthly interest rate:
Monthly interest rate (i) = 5% / 12 = 0.05 / 12 = 0.0041667
Next, calculate the number of monthly payments:
Number of monthly payments (n) = 12 years * 12 = 144
Now, substitute the values into the formula:
M = 54112 [0.0041667(1 + 0.0041667)^144] / [(1 + 0.0041667)^144 - 1]
Calculating this expression, we find:
M = 54112 [0.0041667(1.0041667)^144] / [(1.0041667)^144 - 1]
M ≈ 54112 [0.0041667(1.7367711)] / [1.7367711 - 1]
M ≈ 54112 [0.0072366] / [0.7367711]
M ≈ 54112 * 0.0098342 / 0.7367711
M ≈ 532.1960
Rounded to two decimal places, the monthly payment for a student loan of $54,112 at a fixed APR of 5% for 12 years is approximately $532.20.