A buyer with a 15-year, $250,000 loan at a 5.5% interest rate has a monthly principal and interest payment totaling $2,042.71. What's the total amount the borrower will pay back over the life of the loan?

First, multiply the monthly payment ($2,042.71) by the total number of payments (180 = 12 payments/year for 15 years). The total paid back is $367,687.80. Then subtract the original loan value: $367,687.80 ‒ $250,000 = $117,687.80.

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chilljain33 chilljain33 · Answer 2 · 2022-01-15T05:49:00+01:00

The correct statement will be that the total amount paid by the borrower will be amounting to $367,687.8. The calculation is done over a loan of $250,000 where the monthly payment is $2042.71.

The calculation of the total amount to be paid can be done by multiplying the total monthly payments with the period of loan, which will converted in number of months.

Calculation of Annuity

The formula for the calculation of annuity is,

[tex]\rm Compounded\ Annuity= P(1+ \dfrac{r}{n})^n^t[/tex]

However, we have been given the monthly payments in this example, so we will calculate the annuity by simple multiplication of monthly payment with the number of months.

[tex]\rm Number\ of\ Months= 15 x\ 12\\\\\\\rm Number\ of\ Months=180\ Months[/tex]

So,

[tex]\rm Compounded\ Annuity= 180\ x\ \$2042.71\\\\\rm Compounded\ Annuity= \$367687.8[/tex]

Hence, the total amount of annuity that will be paid on a loan of $250,000 over a course of 15 years will be $367687.8.

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