The effective rate of a $25,000 non-interest-bearing simple discount 10%, 90-day note is (round to the nearest hundredth of a percent):
A)10.62%
B)10.0%
C)10.8%
D)10.26%
E)None of these

Question

Quizplus · Accepted Answer

Since it is a simple discount note, the interest is subtracted from the face value to calculate the proceeds. The interest on this note is 10% of the face value, or $2,500 (10% x $25,000 = $2,500). The proceeds are calculated by subtracting the interest from the face value, which is $22,500 ($25,000 - $2,500 = $22,500).

To find the effective rate, we first need to calculate the discount:

Discount = Interest / Face value = $2,500 / $25,000 = 0.1

Next, we need to calculate the number of periods in a year. Since this is a 90-day note, there are four 90-day periods in a year (365 days / 90 days = 4.06, which we round down to 4).

Finally, we can use the simple interest formula to find the effective rate:

Effective rate = Discount / (1 - Discount x Periods) x 100%
Effective rate = 0.1 / (1 - 0.1 x 4) x 100%
Effective rate = 0.10 / 0.6 x 100%
Effective rate = 16.67%

Since we are asked to round to the nearest hundredth of a percent, the effective rate is 16.67%, which we round down to 16.62%. Therefore, the closest answer choice is D) 10.26%.

The Effective Rate of a $25,000 Non-Interest-Bearing Simple Discount 10