Question

High Rate - 2.410%

Investment Rate - 2.458%

Price per $100 - 99.390806

This is a 91-day T-bill with par value $100 issued on January 10, 2019 and maturing on April 11, 2019.

(a) Calculate the rate of interest that a purchaser of this bill would earn over the period, and convert this to an annual investment rate. Verify that your answer corresponds to the published investment rate.

(b) Calculate the discount rate and verify that your answer corresponds to the published high rate.

(c) Determine how much the investor would have paid for this asset if the investment rate was 1.5%. (Round to two decimal places)

(d) Determine how much the investor would have paid for this asset if the discount rate was 1.5%. (Round to two decimal places)

Answer 1

(a) Cash Outflow on Jan 10, 2019 = Price of T-Bill = $ 99.390806 and Cash Inflow on April 11, 2019 = $ 100

Tenure = 91 days and Number of Days in a Year = 365 (assumed)

Let the rate of interest earned be Re

Therefore, 99.390806 x [1+Re] = 100

Re = [100/99.390806] - 1 = 0.006129 or 0.6129 %

Annualized Re = (0.006129)*(365/91) = 0.02458 or 2.458%

(b) Let the discount rate be Rd

Therefore, 100 x [1-Rd] = 99.390806

Rd = 1- [99.390806/100] = 0.006092 or 0.6092 %

Annualized Rd = (0.6092) x (360/91) = 0.0241 or 2.41 %

NOTE: Rate of Return is expressed using a 365 day year whereas discount rates are based on a 360 day year

(c) Investment Rate = 1.5 %

Maturity Payout = $ 100, Tenure = 91 days and let the price be $ P

Therefore, P x [1+(0.015) x (91/365)] = 100

P = 100 / 1.00374 = $ 99.6274 ~ $ 99.63

(d) Discount Rate = 1.5 %, Maturity Payout = $ 100, Tenure = 91 days and Let the price be $ N

Therefore, 100 x [1-(0.015) x (91/360)] = N

N = $ 99.62083 ~ $ 99.62