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kondor19780726 [428]
3 years ago
11

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?
Business
1 answer:
choli [55]3 years ago
3 0

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.

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<h3>The complete question: </h3>

A publisher has copies of a philosophy book in its inventory, but it produces 1,000 copies of the book in august that it expects to sell in the upcoming academic year. the price of the book is $120. if the publisher actually sells 1,300 textbooks, then:

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