Question

Five years ago you took out a 30- year mortgage with an APR of 6.20% for $206,000. If you were to refinance the mortgage today for 20 years at an APR of 3.95%, how much would you save in total interest expense?

A) $200,503 B) $100,251 C) $150,377 D) $50,126

please show how to calcuated it step by step, thanks!

Answer 1

Solution: 100,251

Working:

Current Mortgage Payment: P/Y =12, N =12* 30 years = 360, I/Y =6.20/12 = 0.51667%, PV = $206,000

PMT = 206,000(A/P, 0.51667%, 360) = 206,000 * 0.0061 = 1261.69

Current Mortgage Balance: P/Y = 12, N = 12* (30 Years - 5 Years) = 300, I/Y =6.20/12 = 0.51667%, PMT = 1261.69,

Solve for PV = 1261.69 (P/A, 0.51667%, 300) = 1261.69 * 152.3039 = $192,159.69

On Current Mortgage the remaining payments = 300 * $1261.69 = $378,505.83

New Mortgage Payment: P/Y = 12, N = 240, I/Y = 3.95/12 = 0.32917%, PV = $192,159.69

Solve for PMT = 192,159.69 (A/P, 0.32917%, 240) = 192,159.69 * 0.0060 = $1159.39

Total Payments on New Mortgage: 240 * $1159.39 = $278,254.4

Differenential in the Payments = [$378,505.83 - $278,254.41] = $100,251