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5 August, 23:09

Seven years ago, Carlos took out a 30-year mortgage for $185,000 at 5.6 percent. He has made all of the monthly payments as agreed. What is his current loan balance

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  1. 5 August, 23:37
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    Remaining balance of loan after 7 years (today) = $ 164,619.6

    Explanation:

    amount of mortgage = $ 185,000

    original term of loan 30 years * 12 = 360 months

    interest rate = 5.6 % * 1/12 = 0.4666% per month

    monthly payment = amount oa mortgage * i / [ 1 - (1+i) ^-n ]

    = $ 185,000 * 0.4666% / [ 1 - (1 + 0.4666%) ^-360 ]

    = $ 863.21 / [ 1 - 0.187148 ]

    = $ 863.21 / 0.812852

    = $ 1061.95

    after 7 years, that means 84 months, remaining term = 360 months - 84 months = 276 months

    remaining balance of loan = amount of loan * (1 + i) ^n - monthly payment * [ { (1 + i) ^n - 1 } / i ]

    remaining balance of loan after 7 years (84 months) = [ $ 185,000 * (1+0.4666%) ^84 ] - $ 1061.95 * [ { (1+0.4666%) ^84 - 1} / 0.4666 ]

    = [ $ 185,000 * 1.47850 ] - $ 1061.95 * (0.47850 / 0.4666% ]

    = $ 273,522.5 - $ 1061.95 * 102.55

    = $ 273,522.5 - $ 108,902.9

    = $ 164,619.6

    remaining balance of loan after 7 years (today) = $ 164,619.6
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