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13 September, 09:24

You are thinking of purchasing a house. The house costs $350,000. You have $50,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offering a 30-year mortgage that requires monthly payments and has an APR of 6% per year. What will your monthly payment be if you take this mortgage? how much interest is paid off in your first mortgage payment?

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  1. 13 September, 11:50
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    Monthly repayment (P) = $1,798.65

    Interest Paid off in First Mortgage = $107,919.09

    Explanation:

    Monthly repayment (P) = rA / [1 - (1+r) ^-n]

    where

    A = Loan Amount

    r = monthly interest rate

    n = loan duration in months

    A = House Cost - down payment

    = $350,000 - $50,000 = $300,000

    r = 6% = 6%/12 = 0.005

    n = 30-years = 30 x 12 = 360 months

    Monthly repayment (P) = 0.005 ($300,000) / [1 - (1+0.005) ^-360]

    Monthly repayment (P) = $1,500 / [1 - (1.005) ^-360]

    Monthly repayment (P) = $1,500 / [1 - 0.166041928]

    Monthly repayment (P) = $1,500 / 0.833958072

    Monthly repayment (P) = $1,798.651575

    Monthly repayment (P) = $1,798.65

    To Calculate Interest Paid off in First Mortgage Payment

    if there is no down payment

    Loan Amoun will be $350,000

    Monthly repayment (P) = rA / [1 - (1+r) ^-n]

    Monthly repayment (P) = 0.005 ($350,000) / [1 - (1+0.005) ^-360]

    Monthly repayment P) = $1,750 / [1 - (1.005) ^-360]

    Monthly repayment (P) = $1,750 / [1 - 0.166041928]

    Monthly repayment (P) = $1,750 / 0.833958072

    Monthly repayment (P) = $2,098.426838

    Monthly repayment (P) = $2,098.43

    Total Payment if loan is $350,000 = $2,098.426838 x 360 = $755,433.6617

    Total Payment if loan is $300,000 = $1,798.651575 x 360 = $647,514.5670

    Interest Paid off in First Mortgage

    Payment = $755,433.6617 - $647,514.5670 = $107,919.0947

    = $107,919.09
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