Question

Suppose you are thinking about purchasing a small office building for $1,500,000. The 30-year fixed-rate mortgage that you have arranged covers 80% of the purchase price and has an interest rate of 8%. Assume you were to default and go into foreclosure in year 10 of this loan. If the lender was able to sell this property for $700,000, how much does the lender stand to lose in the absence of PMI?

Answer is 352,696. Can you please show calculation as to how to get to that answer? Thanks!

Answer 1

Amount of mortgage = 80% * 1,500,000 = 1,200,000

Interest = 8% i.e. (8%/12) monthly

Term = 30 years i.e. 360 months

By using the formula of PV, we get

1,200,000 = Monthly Payment * ((1-(1+(8%/12))^-360)/(8%/12))

Monthly Payment = 1,200,000 * (8%/12) /((1-(1+(8%/12))^-360))

Monthly Payment = $8,805.17

Since loan has been paid for 10 years, we need to determine the amount of loan outstanding at the end of year 10. Amount of loan outstanding at the end of year 10 will be the present value of remaining payments i.e. PV of monthly payments for 240 months

Loan outstanding at the end of year 10 = $8805.17 * ((1-(1+(8%/12))^-240)/(8%/12))

Loan outstanding at the end of year 10 = $1,052,696

Amount recovered from sale of Property = $700,000

Hence amount of loss = amount not recovered

= Loan outstanding at the end of year 10 – amount recovered from sale of property

= $1,052,696 - $700,000

= $352,696

Hence, amount of loss is $352,696