To calculate Garrett's monthly payment for the 20-year $80,000 loan at 7.7% interest compounded monthly, we can use the formula for calculating monthly loan payments:
1. Calculate the monthly interest rate:
- Annual interest rate: 7.7%
- Monthly interest rate: 7.7% / 12 = 0.6417%
2. Determine the total number of payments:
- 20 years * 12 months per year = 240 total payments
3. Use the formula for monthly loan payments:
- Monthly Payment = P[r(1 + r)^n] / [(1 + r)^n - 1]
where:
P = Principal amount of the loan ($80,000)
r = Monthly interest rate (0.6417%)
n = Total number of payments (240)
4. Plug in the values and calculate the monthly payment:
- Monthly Payment = $80,000[0.006417(1 + 0.006417)^240] / [(1 + 0.006417)^240 - 1]
- Monthly Payment ≈ $570.37
Therefore, Garrett's monthly payment for the loan is approximately $570.37 (option C).
