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23 May, 23:58

Assume that you have a balance of $4000 on your credit card and that you make no more charges. If your APR is 23.9% and each month you make only the minimum payment of 5% of your balance, then when is the first time that the balance would be less than $100?

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Answers (2)
  1. 24 May, 01:56
    0
    The balance will be less than $100 after 44 months payment

    Explanation:

    In this question, we are asked to calculate the time at which the Balance on a credit card would be less than $100.

    To calculate this, we proceed as follows;

    The monthly Interest rate = 23.9%/12 = 1.99166667%

    Balance after t months = Credit Card balance * [ (1 + Monthly interest rate) * (1 - Minimum payment rate) ]^t

    The credit card balance is $4,000, and the minimum payment rate is 5%

    We plug these values into the equation to get;

    $4,000 * [ (1+1.99166667%) * (1 - 5%) ]^t

    = $4000 * [1.0199166667 * 0.95]^t

    = $4000 * (0.968920836) ^t

    Balance after t months < 100

    $4,000 * (0.968920836) ^t < 100

    (0.968920836) ^t < 0.025

    t = 43.9 months = 44 months
  2. 24 May, 02:51
    0
    Answer: The balance will be less than $100 after 44 months.

    Explanation:

    We are to calculate the time when the balance on a credit card would be less than $100.

    We were given the following:

    APR = 23.9%

    Monthly Interest rate will therefore be:

    23.9%/12 = 1.99% or 0.0199

    Credit card balance = $4,000

    Minimum payment rate = 5% or 0.05

    The formula is given as:

    Balance after t months = Credit Card balance x [ (1 + Monthly interest rate) x (1 - Minimum payment rate) ]^t

    Therefore:

    $4,000 x [ (1+0.0199) x (1 - 0.05) ]^t

    = $4000 x [1.0199 x 0.95]^t

    = $4000 x (0.97) ^t

    Balance after t months < 100

    = $4,000 x (0.97) ^t < 100

    = (0.97) ^t < 100/4000

    = (0.97) ^t < 0.025

    t = 43.9 months

    t is therefore approximately 44 months.
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