Questions: A student borrows 66,000 at 4.8% compounded monthly. Find the monthly payment and total interest paid over a 30 year payment plan. The payment size is (Round to the nearest cent as needed.) The total interest paid over the 30 years is (Round to the nearest cent as needed.)

Solution Steps

To convert the annual interest rate \(r = 4.8\%\) to a monthly interest rate, we divide by 1200: \[r_m = \frac{r}{1200} = \frac{4.8}{1200} = 0.004\]

The total number of payments \(N\) over the loan term of \(T = 30\) years is calculated by multiplying \(T\) by 12: \[N = T \times 12 = 30 \times 12 = 360\]

Using the formula for an annuity, the monthly payment \(M\) is calculated as: \[M = P \times \frac{r_m \times (1 + r_m)^N}{(1 + r_m)^N - 1} = 66000 \times \frac{0.004 \times (1 + 0.004)^360}{(1 + 0.004)^360 - 1} = 346.28\]

The total amount paid over the loan term is the monthly payment \(M\) multiplied by the total number of payments \(N\): \[Total\ Paid = M \times N = 346.28 \times 360 = 124660.49\]

The total interest paid is the total amount paid minus the principal \(P\): \[Total\ Interest\ Paid = Total\ Paid - P = 124660.49 - 66000 = 58660.49\]

Final Answer