Assume also that you make ONLY the minimum payments. Determine when the balance drops below $200?

Question

You have a balance of $4000 on your credit card, and you make no more charges. Assume that the card requires a minimum payment of 5% and carries an APR of 22.8%. You have a balance of $4000 on your credit card, and you make no more charges. Assume that the card requires a minimum payment of 5% and carries an APR of 22.8%. Assume also that you make ONLY the minimum payments. Determine when the balance drops below $200..

Using Log(

Solve ^t

Answer 1

4000(0.95)^t (1 + 0.228/12)^{(t - 1)} < 200

(0.95)^t (1.019)^(t-1) < 0.05

ln (0.95)^t + ln (1.019)^(t-1) < ln 0.05

t ln (0.95) + (t - 1) ln (1.019) < ln 0.05

-0.051 t + (t - 1)(0.019) < -3.000

-0.051 t + 0.019 t - 0.019 < -3.000

-0,051 t + 0.091 t < -2.981

-0.032 t < -2.981

t > 93.1

You would need more than 93.1 months or 7 years and 10 months.