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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

Answer :

Ojcordelia

Answer:

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)

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