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15 January, 01:45

Charlie cannot remember how much he financed to buy his car. He does remember that his monthly payment is $200. His add-on interest rate was 9% and he made a total of 30 payments. Find the amount of his loan to the nearest penny.

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  1. 15 January, 01:56
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    First find the total payments

    Total paid

    200*30=6,000 (this is the future value)

    Second use the formula of the future value of annuity ordinary to find the monthly payment.

    The formula is

    Fv=pmt [ (1+r/k) ^ (n) - 1) : (r/k) ]

    We need to solve for pmt

    PMT=Fv:[ (1+r/k) ^ (n) - 1) : (r/k) ]

    PMT monthly payment?

    Fv future value 6000

    R interest rate 0.09

    K compounded monthly 12

    N=kt=12 * (30months/12months) = 30

    PMT=6000: (((1+0.09:12) ^ (30)

    -1) : (0.09:12))

    =179.09 (this is the monthly payment)

    Now use the formula of the present value of annuity ordinary to find the amount of his loan.

    The formula is

    Pv=pmt [ (1 - (1+r/k) ^ (-n)) : (r/k) ]

    Pv present value or the amount of his loan?

    PMT monthly payment 179.09

    R interest rate 0.09

    N 30

    K compounded monthly 12

    Pv=179.09 * ((1 - (1+0.09:12) ^ (

    -30)) : (0.09:12))

    =4,795.15

    The answer is 4795.15
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