Question

You received your first credit card with a spending limit of $2,000 at 18.9% interest. You decide you need to upgrade your sound system in your car, so you are going to buy this great deal. The next month you receive your credit card statement and you now owe $2,000. You are able to pay the minimum payment of $100 each month. If you continue paying only $100 each month, how long will it take you to pay off your credit card debt?

Answer 1

It will take approximately 25 months

Explanation:

The amount owed on the credit card statement, P = $2,000

The interest rate of the credit on the credit card, r = 18.9%

The minimum monthly payment made, M = $100

The equal monthly installment formula is given as follows;

`M = (P \cdot \left((r)/(12) \right) \cdot \left(1+(r)/(12) \right)^n )/(\left(1+(r)/(12) \right)^n - 1)`

Therefore, we get;

`100 = (2,000 \cdot \left((0.189)/(12) \right) \cdot \left(1+(0.189)/(12) \right)^n )/(\left(1+(0.189)/(12) \right)^n - 1) = (2,000 *\left(0.01575 \right) \cdot \left(1.01575 \right)^n )/(\left(1.01575\right)^n - 1)`

100×1.01575ⁿ - 100 = 31.50×1.01575ⁿ

100×1.01575ⁿ - 31.50×1.01575ⁿ = 100

68.5×1.01575ⁿ = 100

1.01575ⁿ = 100/68.5

n = ln(100/68.5)/ln(1.01575) ≈ 24.21 (which is approximately 25 months, by rounding up to the nearest whole number)

Therefore, it will take approximately 25 months to pay off the credit card debt