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12 January, 13:07

You plan to buy a $250,000 home with a 20% down payment. The bank you want to finance the loan through suggests two options: a 15-year mortgage at 4.25% APR and a 30-year mortgage at 5% APR. What is the difference in monthly payments between these two options?

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  1. 12 January, 15:35
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    A 15-year mortgage monthly payments is: $1,496.5

    A 30-year mortgage monthly payments is: $1,060.1

    => The difference of monthly payment between the two options is: $436.4 ($1,496.5 - $1,060.1) where the monthly payment of the option of 15-year mortgage is higher.

    Explanation:

    The borrowed amount in both options is : $250,000 * 80% = $200,000;

    * A 15-year mortgage monthly payments is:

    We have (1+APR) = (1 + Monthly Interest rate) ^12 1.0425 = (1 + Monthly Interest rate) ^12 Monthly Interest rate = 0.3475%;

    Amount of payment periods = 15 * 12 = 180

    => Monthly payment = (200,000 * 0.3475%) / [ 1 - 1.003475^ (-180) ] = $1,496.5

    * A 30-year mortgage monthly payments is:

    We have (1+APR) = (1 + Monthly Interest rate) ^12 1.05 = (1 + Monthly Interest rate) ^12 Monthly Interest rate = 0.4074%;

    Amount of payment periods = 30 * 12 = 360

    => Monthly payment = (200,000 * 0.4074%) / [ 1 - 1.004074^ (-360) ] = $1,060.1
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