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18 June, 10:26

You borrow $900 to buy a laptop. You plan to pay off the loan after 5 years of equal monthly payments. After 10 payments, you have $1200 left to pay. What is the simple annual interest rate of your loan?

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  1. 18 June, 10:35
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    Answer: The simple annual interest rate on my loan is 12%

    Step-by-step explanation:

    I planned to pay off the loan after 5 years of equal payments; There are 12 months that make up one year and the total number of months in five years = 12 * 5 = 60 months. This means that I planned to pay off the loan after 60 equal monthly payments.

    If I have also made 10 of such monthly payments already and I have $1,200 left, it means that I now have 50 more months to clear the $1,200 that is left.

    If I have $1,200 left to pay in 50 months, then my average payment per month is =

    $1,200/50 = $24

    Since I pay $24 monthly which includes part of the principal and the interest, then my total payment over the five years (60 months) will be = 24 * 60 = $1,440 (Principal+interest).

    If the principal borrowed was $900, then the interest charged on the money over the 5 years = $1,440 - $900 = $540

    With the interest known, we will now use the simple interest formula to find the simple annual interest rate on the loan.

    Simple interest = (Principal*Rate*Time) / 100

    Where, S. I = $540

    P = $900

    T = 5years

    R = ?%

    540 = (900 * R * 5) / 100

    45R = 540

    R = 540/45

    R = 12%

    Therefore, the simple annual interest rate on my loan is 12%
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