Question

A) Luke-Warm Investments is buying a 120 day original term to maturity bank bill today. The bill matures in 100 days’ time. The bill has a face value of $500,000 and the current yield on this bill is 3%. Note that this is a quoted annual interest rate. How much will Luke-Warm Investments have to pay to buy the bill?

B) After 60 days of holding the bill, Luke-Warm Investments wants to sell the bill on the secondary market. At that time, yields for 60 day bills are 2.65% and 40 day bill yields are 2.50%. How much will Luke-Warm Investments receive when it sells the bill?

Please explain all steps clearly in particular which specific days to use.

Answer 1

Solution :

Face value of the bill =  $500,000, Original maturity time = 120 days , Current maturity time = 100 days

Current yield = 3% per annum

Since these bills are priced at discount based on the interest rate

Part A )

Here the current yield is given as 3% and current maturity time = 100 days so current price of the bill should be discounted using 100 days as maturity

So interest rate for 100 days = 3% * 100 / 365 = 0.00821917808 = 0.821917%

Current price = Face value / (1+ interest rate ) = 500000/ (1.00821917808) = 495,923.62

So, Luke-Warm investment have to pay 495,923.62

Part B )

After holding for 60 days the time to maturity will be 40 days ( 100 days - 60 days )

40 days yield = 2.5% annum

40 days interest = 2.5% * 40 / 365 = 0.273973%

Current price at this interest rate = 500,000 / ( 1+ 0.00273979) = 498,633.88

So, Luke- Warm will receive 498,633.88 when they sell the bill