Question

(Comparing Types of Interest MC)

A college student is paying for tuition through private loans. Two lenders have approved the student for a $25,000 loan.

Offer 1: 5.99% annual simple interest, with a total account balance of $32,487.50 after a 60-month term
Offer 2: 3.75% annual interest compounded monthly for a 66-month term

Assuming no payments are made, what is the difference in the account balances at the end of the loan terms? Round your answer to the nearest penny.

$1,245.00
$1,770.87
$2,964.36
$3,319.94

Answer 1

you have the work?

Answer 2

@sza

Answer 3

we can use the simple interest formula to calculate the balance for Offer 1:

I = P * r * t
I = 25,000 * 0.0599 * 5
I = 7,475

Total account balance for Offer 1 = P + I
Total account balance for Offer 1 = 25,000 + 7,475
Total account balance for Offer 1 = 32,475

For Offer 2, we can use the compound interest formula:

A = P * (1 + r/n)^(n*t)
A = 25,000 * (1 + 0.0375/12)^(12*66/12)
A = 31,692.17

The difference in account balances at the end of the loan terms is:

Difference = Total account balance for Offer 2 - Total account balance for Offer 1
Difference = 31,692.17 - 32,487.50
Difference = -795.33

Rounding to the nearest penny, the difference in account balances at the end of the loan terms is $-795.33. This means that Offer 1 would result in a higher account balance at the end of the loan term.