A realtor sold a house on August 31, 1997 for $150k to a buyer in which a 20% down payment was made. The buyer took a 15yr mortgage on the property with an effective interest rate of 8% per annum. The buyer intends to pay off the mortgage owed in yearly payments starting on August 31, 1998.

Question

A realtor sold a house on August 31, 1997 for $150k to a buyer in which a 20% down payment was made. The buyer took a 15yr mortgage on the property with an effective interest rate of 8% per annum. The buyer intends to pay off the mortgage owed in yearly payments starting on August 31, 1998.
a) How much of the mortgage will still be owed after the payment due in August 31, 2004, has been made?

b) Solve the same problem by separating the interest and the principal amounts.

Can you please show them step by step format so I can learn. thank you.

economyst · Answer

So the loan (B0) was 150*.8 = 120K
The balance after 1 year and 1 payment would be B1=B0*(1.08)-P.
B2=(B1*(1.08)-P = B0*(1.08)^2 - P*(1.08) - P
....
B15 = B0(1.08)^15 - sum(P*(1.08)^i)

Solve for the annual payment P such that B15=0.

An Excel spreadsheet can handle this otherwise tedious calculation rather quickly.