The simple interest note was discounted at 15%. Find the discount period in days and the proceeds.
-Loan made: Apr 18
Face value: $400
Length of loan: 150 days
Rate: 11%
Date of discount: June 18
A)90 days, $406.83
B)89 days, $384.49
C)89 days, $402.82
D)90 days, $388.50

Question

Quizplus · Accepted Answer

The first step is to calculate the interest using the formula:
Interest = Principal x Rate x Time
Interest = $400 x 0.11 x (150/365) = $18.08
The amount to be paid at maturity is:
Maturity Value = Face Value + Interest
Maturity Value = $400 + $18.08 = $418.08
Next, we need to calculate the discount using the formula:
Discount = Maturity Value x Discount Rate x Discount Time
Discount Time = Number of days from the date of discount to the date of maturity
Discount Time = 150 - 31 = 119 days
Discount = $418.08 x 0.15 x (119/365) = $15.26
The proceeds are:
Proceeds = Maturity Value - Discount
Proceeds = $418.08 - $15.26 = $402.82
Therefore, the correct answer is C, 89 days and $402.82. The first step is to find the interest earned on the note:

Interest = Principal x Rate x Time
Interest = $400 x 0.11 x (150/360)
Interest = $18.33

Next, we need to find the discount:

Discount = Face Value x Discount Rate x Discount Time
Discount = $400 x 0.15 x (30/360)
Discount = $5

The proceeds (also known as the discounted value) is simply the face value minus the discount:

Proceeds = Face Value - Discount
Proceeds = $400 - $5
Proceeds = $395

To find the discount period, we need to calculate the number of days between the date of the loan and the date of discount:

June 18 - Apr 18 = 61 days

Then, we need to subtract the discount time (in days) from the total number of days to get the discount period:

Discount Period = Total Days - Discount Time
Discount Period = 61 days - 30 days
Discount Period = 31 days

However, the discount period above is for the banker's year, which is 360 days. To convert it to a regular year of 365 days, we can use the following formula:

Discount Period in Days = (Discount Period in Banker's Year x 365) / 360
Discount Period in Days = (31 x 365) / 360
Discount Period in Days = 31.97 or approximately 32 days

Therefore, the discount period is 32 days, which is closest to choice C. The proceeds is also closest to choice C at $402.82.

The Simple Interest Note Was Discounted at 15