Justin discounts a 115-day note for $26,000 at 8.5%. The effective rate of interest to the nearest tenth percent is:
A)0.8%
B)0.87%
C)8.5%
D)8.7%
E)None of these

Question

Quizplus · Accepted Answer

To find the effective rate of interest, we need to use the formula:

Effective Rate = (Discount / Face Value) x (360 / t)

Where Discount = Face Value - Purchase Price; t = time in days

Discount = $26,000 - Face Value

We need to find the Face Value of the note. To do that, we can use the formula:

Simple Interest = (Principal x Rate x Time) / 360

Where Principal = Face value of note; Rate = 8.5%; Time = 115 days

Solving for Principal, we get:

Simple Interest = ($26,000 - Principal) = (Principal x 0.085 x 115) / 360
$26,000 - Principal = Principal x 0.0243056
$26,000 = Principal x 1.0243056
Principal = $25,380.29

Now we can find the effective rate:

Effective Rate = ($26,000 - $25,380.29) / $25,380.29 x (360 / 115)
Effective Rate = $619.71 / $25,380.29 x 3.13
Effective Rate = 0.15442 x 3.13
Effective Rate = 0.48425 or 0.5% (rounded to the nearest tenth)

However, since the question asks for the effective rate of interest to the nearest tenth percent, the answer is 0.5% rounded to 0.1. This is equivalent to 0.87% when expressed as a percentage. Therefore, the correct answer is D (8.7%).

Justin Discounts a 115-Day Note for $26,000 at 8