Final answer:
To find the scheduled annual payment, we use the loan amount, interest rate, and amortization period in the annuity formula. The loan balance at maturity is determined using the remaining balance after the 10th payment. The effective cost of borrowing includes the origination fee, interest payments, and principal repayment over the 10-year term.
Step-by-step explanation:
To calculate the annual mortgage payment, we use the mortgage amortization formula. For a $7.2M loan with a 5.5% interest rate, 10-year term, and a 25-year amortization period, the mortgage payment can be calculated using an annuity formula.
First, find the periodic interest rate by dividing the annual rate by the number of periods per year, in this case, 5.5% / 1 = 0.055. Next, calculate the annuity factor using the formula for the present value of an annuity: PV = PMT * [(1 - (1 + r)^(-n)) / r], where PV is the loan amount, PMT is the payment, r is the periodic interest rate, and n is the total number of payments (25 years * 1 payment per year = 25).
Using any financial calculator or spreadsheet:
- Enter PV = $7,200,000 (loan amount)
- Enter r = 5.5% annual rate
- Enter n = 25 years
- Calculate for PMT (the payment)
The loan balance at maturity is computed by subtracting the sum of all payments made over the 10-year term from the amortization schedule. We must determine the remaining balance after the 10th payment.
The effective cost of borrowing includes the initial origination fee and the total interest paid over the loan term. Subtract the origination fee from the amount borrowed, and add up all interest payments made over the 10 years, including the principal repayment at maturity to calculate the total cost of borrowing.