Final answer:
To calculate Brittany's monthly payment, convert the annual interest rate to a monthly rate, determine the total number of payments, and use the amortizing loan payment formula. With the given values, a calculator will provide the exact payment amount.
Step-by-step explanation:
To calculate the size of the monthly payments for Brittany's loan of $30,000 at an interest rate of 6.25% compounded monthly over a period of 5 years, we use the formula for the monthly payment (M) of an amortizing loan:
M = P [ i(1 + i)^n ] / [ (1 + i)^n − 1 ]
Where:
- P = principal amount ($30,000)
- i = monthly interest rate (annual rate / 12)
- n = total number of payments (years × 12)
First, calculate the monthly interest rate:
i = 6.25% per year / 12 months = 0.0625 / 12 = 0.0052083
Next, calculate the total number of payments:
n = 5 years × 12 months/year = 60 payments
Now, substitute the values into the formula to find the monthly payment:
M = 30,000 [ 0.0052083(1 + 0.0052083)^60 ] / [ (1 + 0.0052083)^60 − 1 ]
A calculator is needed to compute the exact monthly payment. The resulting figure will be the amount Brittany needs to pay each month to settle the loan at the end of 5 years.