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Frank purchased his house 16 years ago by taking out a 25-year mortgage for $150,000. The mortgage has a fixed interest rate of 5 percent compounded monthly. If he wants to pay off his mortgage today, how much money does he need? He made his most recent mortgage payment earlier today. (Round your intermediate calculation and your answer to two decimal places.)

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hoangkhangpham94

Answer:

The answer is $76,312.05

Explanation:

We have monthly interest rate which is discount rate is: 5% / 12 = 0.42%;

The mortgage will have 25 x 12 = 300 payments;

The monthly payment is calculated by applying present value for annuity as below:

(150,000 x 0.42%) / [ 1 - (1+0.42%)^(-300)] = $880.38

As at the time of fully pay-off, there are (25-16) * 12 = 108 payments left.

The amount needs to fully pay-off this loan is equal to the present value of 108 payments left which is calculated as below:

(880.38/0.42%) * (  [ 1 - (1+0.42%)^(-108)] = $76,312.05.

So, the answer is $76,312.05.

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