Answer:
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.
