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

B - $100,251

Explanation:

Formula for monthly repayments: M = P [ {r * (1 + r) ∧n} / { (1 + r) ∧n - 1}]

Where M = monthly repayments

P = principal

r = monthly interest rate, calculated by dividing annual rate by 12 i. e. 6.20%/12

n = number of monthly repayments i. e. 30 * 12

Current mortgage repayment:

M = 206000 [ {0.062/12 * [1 + (0.062/12) ∧360]} / {[ (1 + (0.062/12) ]∧360 - 1} ]

≈ $1262

Current mortgage balance:

calculating P where n = 25 * 12 (after 5 years) = 300

1262 = P [ {0.062/12 * [1 + (0.062/12) ∧300]} / {[ (1 + (0.062/12) ]∧300 - 1} ]

P ≈ $192,160

Total remaining payments on current mortgage = 300 * $1262 = $378,600

Refinancing would mean: n = 20 * 12 = 240

r = 3.95% / 12

M = 192,160[ {0.0395/12 * [1 + (0.0395/12) ∧240]} / {[ (1 + (0.0395/12) ]∧240 - 1} ]

≈ $1160

Total payments on new mortgage = 240 * 1160 = $278,400

Savings on Refinancing: $378,600 - $278400 = $100,200 (approximately)