Solve the problem.
-Jerry Jones buys a $120,000 T-bill at a 5.8% discount for 30 weeks. Find the interest earned on the T-bill. (Assume 52 weeks per year.)
A)$4,416.92
B)$2,007.69
C)$4,015.38
D)$8,030.77

Question

Quizplus · Accepted Answer

The amount paid for the T-bill is calculated by subtracting the discount from the face value:
$120,000 - 0.058($120,000) = $113,040
The interest earned is the difference between the amount paid for the T-bill and the face value, which is also the amount to be repaid at maturity:
$120,000 - $113,040 = $6,960
To find the annual interest rate, we need to adjust for the fact that the T-bill has a 30-week maturity rather than a full year. We can do this by dividing the interest earned by the amount paid for the T-bill, and then multiplying by the ratio of weeks per year:
($6,960 / $113,040) * (52/30) = 0.064
So the annual interest rate is 6.4%. Finally, we can calculate the interest earned over 30 weeks by multiplying the amount paid for the T-bill by the weekly interest rate and the number of weeks:
$113,040 * (0.064 / 52) * 30 = $4,015.38 To find the interest earned on the T-bill, we need to first find the purchase price of the T-bill.

Purchase price = face value × (1 – discount rate × time in years)

The face value of the T-bill is $120,000, the discount rate is 5.8%, and the time in years is 30/52 (since there are 52 weeks in a year).

Purchase price = $120,000 × (1 – 0.058 × 30/52) ≈ $113,984.62

Next, we can find the interest earned by subtracting the purchase price from the face value:

Interest = face value – purchase price = $120,000 – $113,984.62 ≈ $6,015.38

Therefore, the interest earned on the T-bill is $6,015.38, which is closest to choice C, $4,015.38.

Solve the Problem. -Jerry Jones Buys a $120,000 T-Bill at a 5.8% Discount