Question

A 285-day T-bill is currently selling for $941.7. What are the (a) discount rate and (b) investment rate?

Answer 1

Solution

The information provided in the problem is as follows,
Maturity Period (n) = 285 Days
Purchase Price (P) = $941.70
Assuming, Nominal Value (NV) = $1,000,
and, 1 Year = 360 Days

Now, we know that, P = NV - Discount, where Discount = NV x Discount Rate (d) x (n / 360)
Therefore,
P = NV - Discount
Or, P = NV - [NV x d x (n / 360)]
Or, P = NV x {1 - [d x (n / 360)]}
Now replacing with the given values,
941.70 = 1000 x {1 - [d x (285/360)]}
Or, 941.70 = 1000 x (1 - 0.7917d) [(285/360) = 0.7917 (Approx.)]
Or, 1 - 0.7917d = 0.9417
Or, 0.7917d = 1 - 0.9417
Or, d = 0.0583 / 0.7917
Or, d = 0.07364 (Approx.)

Therefore, Discount Rate = 7.364%

To calculate Investment rate (IR), we will use the following equation,
IR = (360 x d) / [360 - (n x d)]
Replacing the values we get,
IR = (360 x 7.364%) / [360 - (285 x 7.364%)]
= 26.5104 / (360 - 20.9874)
= 26.5104 / 339.0126
= 0.0782 (Approx.)

Therefore, Investment Rate = 7.82%

Answer: The Discount Rate is 7.364% and the Investment rate is 7.82%