Ten years ago, you took out a $500,000 loan to buy a small apartment building. The loan had a 6.25% interst rate, 25-year amortization and, like all mortgage loans, had monthly payments and interest compounding. Currently, mortgage rates have declined so that you could refinance the current loan balance with a new loan having a 5.75% interest rate and 20 year amortization period. You intend to own the property for 5 more years and are considering refinancing. a) Calculate the payments on the original loan b) Calculate the current loan balance of the original loan c) Calculate the loan balance of the original loan 5 years from now. d) Using the current, lower interest rate, calculate the present value of the remaining original loan payments (i. e. the PV of 60 monthly loan payments and the repayment of the loan balance after 5 years) e) Assume you refinance, taking out a new loan at the lower rate with an initial balance equal to the current balance of the original loan (i. e. the new loan amount is your answer from part b). Calculate the payments on this new loan. f) Calculate the loan balance of the new loan 5 years from now.

a) Calculate the payments on the original loan

monthly payment = principal / annuity factor

principal = $500,000

PV annuity factor, 300 periods, 0.52% = 151.59095

monthly payment = $500,000 / 151.59095 = $3,298.349934 ≈ $3,298.35

b) Calculate the current loan balance of the original loan

I prepared an amortization schedule on an excel spreadsheet. The balance after the 120th payment is $384,681.

c) Calculate the loan balance of the original loan 5 years from now.

the balance after the 180th payment = $293,760

d) Using the current, lower interest rate, calculate the present value of the remaining original loan payments

we can use the present value of an ordinary annuity formula to determine the present value of the remaining 60 payments (of $3,298.35 each) and the present value of $293,760.

PV of loan payments = $3,298.35 x 52.0404 (PV annuity factor, 0.479%, 60 periods) = $171,647.45

PV of principal = $293,760 / (1 + 5.75%)⁵ = $222,121.59

total = $393,769.04

e) Assume you refinance, taking out a new loan at the lower rate with an initial balance equal to the current balance of the original loan (i.e. the new loan amount is your answer from part b). Calculate the payments on this new loan.

monthly payment = principal / annuity factor

monthly payment = $384,681 / 142.43323 = $2,700.78

f) Calculate the loan balance of the new loan 5 years from now.

I prepared a second amortization schedule (modified amortization schedule). The principal balance after the 60th payment is $325,235

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