Question

please do not do this in an excel

6, Joe bought a house for $300,000 and made a $60,000 down payment. He obtained a 20-year loan for the remaining amount. Payments were made monthly. The interest rate was 6%, compounded monthly. After 12 years (144 payments), he decided to refinance the loan at a current rate of 4.8%, compounded monthly. Given that Joe refinances over the remaining period of the original loan, the most he is willing to pay for refinance charges is closest to (4) a) $6,647 b) $7,500 c) $8,320 d) $5,717 e) $6,251 ) $7,748 8) S6,000 h) $7,237

Answer 1

House value = 300000

Downpayment = 60000

Loan = 300000 - 60000 = 240000

i = 6% compounded monthly = 6%/12 = 0.5% per month

t = 20 years = 20*12 = 240 months

Monthly payment = 240000*(A/P,0.5%,240) = 240000 * 0.0071643 = 1719.432

Payments left after 144 payments = 240-144 = 96

Principal due after 144 payments = 1719.432*(P/A, 0.5%,96) = 1719.432 * 76.095218 = 130840.553

Refinance interest rate = 4.8% = 4.8%/12 = 0.4% monthly

Monthly payment = 130840.553 * (A/P,0.4%,96) = 130840.553 * 0.0125649 = 1643.998

Saving in monthly payment = 1719.432-1643.998 = 75.433

Total savings = 775.433 * 96 = 7241.62 = 7242

This is the maximum he will pay for refinance charges

This is closest to option g) 7237, so correct answer is option g