With only a part-time job and the need for a professional wardrobe, Rachel quickly maxed out her credit card the summer after graduation. With her first full-time paycheck in August, she vowed to pay $260 each month toward paying down her $10 comma 574 outstanding balance and not to use the card. The card has an annual interest rate of 16 percent. How long will it take Rachel to pay for her wardrobe? Should she shop for a new card? Why or why not?

a. It will take her 5 years to pay for her wardrobe

b. She should shop for a new card once she is done paying for this one.

c. She should shop for a new card after finishing paying for this card since going further into debt with the current card would be a bad idea. This is due to the fact that an annual interest rate of 16% is very high. The best option would therefor to finish her payments on the credit card, then shop for a new card with a lower annual interest rate.

Explanation:

Use the formula below to determine the number of months it would take Rachel to pay off her debt;

C * {1 - (1+r) ^ (-n*t) } / (r/n) = PV

where;

C=annuity

r=annual interest rate

n=number of compounding periods in a year

t=number of years

PV=present value

In our case;

PV=$10,574

C=$260

r=16%=16/100=0.16

n=12

t=unknown

replacing;

260*{1 - (1+0.16/12) ^ (-12*t) } / (0.16/12) = 10,574

1 - (1+0.16/12) ^ (-12*t) = {10,574 * (0.16/12) }/260

1-{1.013^ (-12 t) }=0.542

(1-0.542) = 1.013^ (-12 t)

ln 0.458=-12 t (ln 1.013)

t=-ln 0.458/12*ln 1.013

t=5

It will take her 5 years to pay for her wardrobe

b. She should shop for a new card once she is done paying for this one.

c. She should shop for a new card after finishing paying for this card since going further into debt with the current card would be a bad idea. This is due to the fact that an annual interest rate of 16% is very high. The best option would therefor to finish her payments on the credit card, then shop for a new card with a lower annual interest rate.