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5 July, 16:08

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

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  1. 5 July, 18:22
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    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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