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30 May, 00:54

What is the remaining balance on a 30-year, $400,000 mortgage after 70 months? Assume monthly payments and a nominal rate (monthly compounding) of 5.90%.

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  1. 30 May, 01:10
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    Answer: The loan balance after 70 months will be $ 366184.45

    Explanation:

    r = 0.059/12

    Present Value (Pv) = 400000

    n = 30 x 12 = 360

    Monthly Payments = rPv / (1 - (1+r) ^-n)

    Monthly Repayments = (0.059/12) x 400000 / (1 - (1+0.059/12) ^-360)

    Monthly Repayments = 1966.66664/0.828926661 = 2372.5460074

    Monthly Repayments = 2372.55

    Loan Balance = PV (1+r) ^n - P ((1+r) ^n - 1) / r

    = 400000 (1+0.059/12) ^70 - 2372.55 ((1+0.059/12) ^360 - 1) / 0.059/12

    = 563849.79539 - 197665.34102 = 366184.4543

    The loan balance after 70 months will be $ 366184.45
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