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23 February, 14:03

Cynthia has the choice of taking out a 25-year loan for $155,000 at 4.4% interest, compounded monthly, or the same loan at 20 years for a higher monthly payment. If she would pay a total of $100,831 in interest on the 25 - year loan, how much in total would she pay in interest on the 20-year loan?

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  1. 23 February, 14:25
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    Answer: Less than $100,831

    Step-by-step explanation:

    There is an equation for the calculation monthly payment which is:

    x = p * r * (1+r) ^n / (1+r) ^n - 1

    where,

    p = the amount of loan, which is $155,000.

    r = monthly interest rate, which is (4.4/12) / 100 = 0.00367

    n = number of months for paying back, which is 20 * 12 = 240

    Since we have all the values, we plug them in and solve.

    x = 155,000 * 0.00367 * (1.00367^240) / (1.00367^240) - 1

    x = $972.27

    Therefore, the monthly payment is approximately $972.3. We csn now multiply it by the number of months in order to get total payment:

    $973.3 * 240 = $233,352

    Therefore, the total amount, which is the loan plus the interest, will be 233,352 dollars.

    To find the amount of interest, we subtract the loan from total amount:

    = $233,352 - $155,000

    = $78,352
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