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21 December, 00:14

Immediately after graduating you bought a car with a bank loan of $20,000. The term of the loan is 5 years with monthly payments at an interest rate of 12% compounded monthly. a) What is the amount of the twelfth payment goes to pay interest?

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  1. 21 December, 00:29
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    Principal borrowed = $20,000

    Loan year=5years

    Monthly interest = 12%

    We need to find the amount after 12years

    Compound interest is give as

    Using compound interest formula

    A=P (1+r/n) ^nt

    Where,

    P = principal amount = $20,000

    r = annual rate of interest = 12%=0.12

    t = number of years the amount invested = 5years

    A = amount of money accumulated after n years, including interest.

    n = number of times the interest is compounded per year=12months

    Therefore,

    A=P (1+r/n) ^nt

    A=20,000 (1+0.12/12) ^5*12

    A=20,000 (1+0.01) ^60

    A=20,000 (1.01) ^60

    A=20,000*1.817

    A=$36,333.9

    So he is meant to pay $36,333.9 for 5years (60months)

    Then he will pay

    $36,333.9/60

    He will pay $605.57 per month

    So his twelfth payment is 605.47*12=$7266.78

    Using is normal payment

    He is suppose to pay $20,000 at a rate of $20,000/60=333.33

    Then after the twelve payment, then he his supposed to pay $333.33*12=$4000

    So the interest between on the twelfth payment is 7266.78-4000 = $3266.9
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