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?

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

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.