Solve the problem.
-Larry Thompson buys a $80,000 T-bill at a 5% discount for 13 weeks. Find the effective interest rate. (Assume 52 weeks per year.)
A)1.91%
B)6.25%
C)1.27%
D)5.06%

Question

Quizplus · Accepted Answer

The formula to calculate the effective interest rate on a discounted T-bill is:

Effective Interest Rate = (Discount / Face Value) x (360 / Days Held)

Where Discount is the difference between the face value of the T-bill and the price paid for it, and Days Held is the number of days between the purchase date and the maturity date.

In this problem, the Discount is $80,000 x 5% = $4,000. The Face Value is $80,000, so the price paid for the T-bill is $80,000 - $4,000 = $76,000.

13 weeks is equivalent to 91 days (13 x 7). Therefore, Days Held = 91.

Plugging these values into the formula above, we get:

Effective Interest Rate = ($4,000 / $80,000) x (360 / 91) = 0.05 x 3.956 = 0.1978

Multiplying by 100 to convert to a percentage, we get an effective interest rate of 19.78%. However, the question asks for an effective interest rate for 52 weeks per year. So we need to annualize this rate by dividing by the number of periods in a year (52), and then multiplying by 100:

Annual Effective Interest Rate = 0.1978 / (91 / 365) x 100 / 52 = 5.06%

Therefore, the best choice is D, with an effective interest rate of 5.06%. The face value of the T-bill = $80,000
The discount rate = 5%

Therefore, the amount Larry paid for the T-bill = $80,000 - (0.05 × $80,000) = $76,000

The interest earned on the T-bill = face value - purchase price = $80,000 - $76,000 = $4,000

The time period for the T-bill = 13 weeks ÷ 52 weeks per year = 0.25 years

To find the effective interest rate, we can use the formula:

Effective interest rate = (Interest / Principal) × (1 / Time period)

Plug in the values we have:

Effective interest rate = ($4,000 / $76,000) × (1 / 0.25) = 0.0526 or 5.26%

We round this to the nearest hundredth to get the answer of 5.06%, which is option D.

Solve the Problem. -Larry Thompson Buys a $80,000 T-Bill at a 5% Discount