Question

A​ lump-sum loan of​ $5,000 is needed by Chandra to pay for college expenses. She has obtained small consumer loans with 1212​% interest per year in the past to help pay for college. But her father has advised Chandra to apply for a PLUS student loan charging only​ 8.5% interest per year. If the loan will be repaid in full in five​ years, what is the difference in total interest accumulated by these two types of student​ loans?

Answer 1

Answer:

Ans. The difference between the two student loans is $1,340.73, in other words, if Chandra picks the small consumer loan, she would have to pay $1,340.73 more in interest.

Explanation:

Hi, first, we need to find out the future value of both loans and then substract the principal to know how much interest Chandra would pay for each. From there, we just find the difference.

The formula to know the future value of both credit is:

$FutureValue=PresentValue(1+r)^{n}$

Where:

r= the interest rate

n= the years of the loan

Let´s find out the future value of the small consumer loan.

$FV(comsumer)=5,000(1+0.1212)^{5}=8,859.02$

Now let´s find out how much interest would Chandra pay.

$Interest(consumer)=8,859.02-5,000=3,859.02$

Now, let´s see what it is going to be the final balance of the loan if Chandra would have picked the PLUS loan.

$FV(PLUS)=5,000(1+0.085)^{5} =7,518.28$

And its interest are:

$Interest(PLUS)=7,518.28-5,000=2,518.28$

The difference is then:

$Difference=Interest(consumer)-Interest(PLUS)$

$Difference=3,859.02-2,518.28=1,340.73$

This means that she will pay $1,340.73 more in interest if she picks the small consumer loan.

Best of luck.