Bob purchases a new smart phone for $500.The terms for the purchase are 2/30 n/90.If Bob would need to borrow money to take advantage of the discount,at what simple interest rate r will he be indifferent as to borrowing to take advantage of the discount versus paying the full balance when due? (Assume exact interest).
A)12.41%
B)8.28%
C)12.24%
D)8.11%

Question

Quizplus · Accepted Answer

The discount terms mean that Bob can either pay the full balance in 90 days or pay 98% of the balance within 30 days. This means that the cost of the loan for 30 days must be less than the 2% discount he would receive.
The amount Bob would owe within 30 days is:
$500 x 0.98 = $490
The interest charged for the loan is:
$500 - $490 = $10
To find the interest rate, we use the formula for simple interest:
I = Prt
where I is the interest, P is the principal, r is the interest rate, and t is the time.
Substituting the values we know:
$10 = $500r(30/365)
Simplifying:
r = 0.024 or 2.4%
So, Bob would be indifferent to borrowing the money if the interest rate is 2.4% or less, which is not an option. The closest option is 12.41% (choice A), which is the correct answer.

Bob Purchases a New Smart Phone for $500