Question

In August 2004, Bonnie Martin bought a house for $391,000. She put 20% down and financed the rest with a thirty-year loan at the then-current rate of 5 3 4 %. In 2007, the real estate market crashed. In June 2009, she had to sell her house. The best she could get was $235,000. Was this enough to pay off the loan?I got no. If so, how much did she profit? If not, how much did she have to pay out of pocket to pay off the loan? (Round your answer to the nearest cent.) I got 76150.53 which is incorrect

Answer 1

Bonnie Martin's cost of the house = $391,000

Down payment = 20% of cost of house $391,000 =$78,200

Therefore, loan amount = Cost of the house - Down payment

= $391,000 - $78,200= $312,800

We can use PV of an Annuity formula to calculate the monthly payment of home loan

PV = PMT * [1-(1+i) ^-n)]/i

Where PV = $312,800

PMT = Monthly payment =?

n = N = number of payments = 30 years *12 months =360 month

i = I/Y = interest rate per year = 5 3/4% = 5.75%, therefore monthly interest rate is 5.75%/12 = 0.479% per month

Therefore,

$312,800= PMT* [1- (1+0.00479)^-360]/0.00479

= $1,825.42

Monthly payment is $1,825.42

Now to calculate loan balance in June 2009 or after 58 months; we can again use PV of an Annuity formula to calculate present value of home loan

PV = PMT * [1-(1+i) ^-n)]/i

Where PV after 58 months =?

PMT = Monthly payment = $1,825.42

n = N = number of payments = 30 years *12 months =360 month – 58 months = 302 months

i = I/Y = interest rate per year = 5 3/4% = 5.75%, therefore monthly interest rate is 5.75%/12 = 0.479% per month

Therefore,

PV = $1,825.42 * [1- (1+0.00479)^-302]/0.00479

= $291,024.04

Therefore the balance on house loan in June 2009 or after 58 months is $291,024.04

But the best price of house she could get was $235,000

Therefore it was not enough to pay off the loan

The amount that she have to pay out of pocket to pay off the loan = Therefore the balance on house loan in June 2009 - the best price of house she could get

= $291,024.04 -$235,000

= $56,024.04

Therefore the amount of $56,024.04, she has to pay out of pocket to pay off the loan.