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23 May, 22:35

Thom owes $5,000 on his credit card. The credit card carries an APR of 17.3 percent compounded monthly. If Thom makes monthly payments of $170 per month, how long will it take for him to pay off the credit card assuming that he makes no additional charges

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  1. 24 May, 00:52
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    39 months

    Explanation:

    loan balance $5,000

    APR = 17.3% compounded monthly / 12 = 1.44167% monthly interest rate

    monthly payment = $170

    if we use the present value of annuity formula:

    PV = payment x ({1 - [1 / (1 + r) ⁿ]} / r)

    5,000 = 170 x ({1 - [1 / (1 + 0.0144167) ⁿ]} / 0.0144167)

    29.4118 = {1 - [1 / (1.0144167) ⁿ]} / 0.0144167

    0.42402 = 1 - [1 / (1.0144167) ⁿ

    1 / (1.0144167) ⁿ = 0.57598

    1.0144167ⁿ = 1 / 0.57598 = 1.73617

    n log1.0144167 = log1.73617

    n 0.00621639 = 0.2395926

    n = 0.2395926 / 0.00621639 = 38.54 ≈ since the payments must be made in full months, we have to round up to 39 months

    to check our answer:

    PV = payment x ({1 - [1 / (1 + r) ⁿ]} / r)

    PV = 170 x ({1 - [1 / (1 + 0.0144167) ³⁹]} / 0.0144167)

    PV = $5,044.36
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