Jay discounts a 100-day note for $25,000 at 13%. The effective rate of interest to the nearest hundredth percent is:

Question

Quizplus · Accepted Answer

To find the effective rate of interest, we need to first find the present value of the note using the formula:

present value = face value / (1 + (rate x time)/360)

where rate and time are both in days.

In this case, the present value is:

present value = 25,000 / (1 + (0.13 x 100)/360) = 22,002.32

The interest earned is the difference between the face value of the note and the present value:

interest = 25,000 - 22,002.32 = 2,997.68

The effective rate of interest is the annualized interest rate that would give the same total interest on a loan with the same principal and term. To find this rate, we can use the formula:

effective rate = (interest / present value) x (360 / time)

In this case, the effective rate is:

effective rate = (2,997.68 / 22,002.32) x (360 / 100) = 0.1221 x 3.6 = 0.4396

Converting to a percentage, we get:

effective rate = 13.496% (rounded to the nearest hundredth)

Jay Discounts a 100-Day Note for $25,000 at 13