Question

Sebastian and Caroline obtained a 30-year, fixed rate mortgage for $154,850 on a home that cost them $169,900. If the interest rate on the mortgage is 5.57%, what is the total cost of the principal and interest at the end of the mortgage?

Answer 1

$318,972.30

Explanation:

The total of 360 payments will be $318,972.30.

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A financial calculator or app is useful for answering questions like this. Most spreadsheets have functions that will serve the same purpose.

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You may be given a formula for computing the monthly payment (A) from the principal (P), the annual interest rate (r) and the number of years (t). It might look like this:

A = P·(r/12)/(1 -(1 +r/12)^(-12·t))

Filling in the given numbers, you get ...

A = 154,850·(0.0557/12)/(1 -(1 +0.0557/12)^-360) ≈ 886.034154

Then the value of 360 such payments is ...

P+I = 360·886.034154 ≈ 318,972.30

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In practice, the final payment will be different from the rest, to make up for the fact that the value of each payment was rounded down to the nearest cent. Rather than try to figure the amount of that payment, we have used a more precise value for the monthly payment and have assumed that doing so will give approximately the same total as the sequence of actual payments. (Our number here is about $2.34 low.)