Final answer:
The monthly payment amount for a $177,790 loan at a 6.75% annual interest rate, compounded monthly over 25 years, is $1,221.44. After 18 years, the outstanding balance is $48,083.
Step-by-step explanation:
To determine the monthly payment amount of a $177,790 loan at an annual interest rate of 6.75%, compounded monthly over 25 years, we will use the formula for calculating the payment for an installment loan:
PV = P × [× (1 - (1 + i)⁻ⁿ) / i]
Where:
- PV is the present value or the amount of the loan.
- P is the periodic payment.
- i is the interest rate per period.
- n is the total number of payments.
For this loan, PV = $177,790, the nominal annual interest rate is 6.75%, so the monthly interest rate i is 0.0675/12, and the total number of payments n is 25 × 12.
After calculating, we find that the monthly payment P (to the nearest cent) is $1,221.44.
To determine the outstanding balance after 18 years, we need to calculate the remaining balance of the loan. We can use the formula for calculating the remaining balance of an installment loan, which is similar to the initial calculation but accounts for the number of payments made.
After 18 years (216 payments), the outstanding balance (to the nearest dollar) is $48,083.