Question

Question 18 (2 points) A $100,000, 168-day T-bill was purchased on the issue date for a price that would earn the investor a simple interest rate of 4.17% per annum if held until maturity. The investor sold the note after 30 days at a price that would yield the purchaser a simple interest rate of 4.81% per annum if held until maturity. Calculate the simple interest rate earned by the original investor during the time that they held the T-bill. Express your answer as an annual percentage rate rounded to 2 decimal places. Do not include the % sign. Your Answer:

Answer 1

Given :

T-Bill Face Value : $100,000

Duartion of the bill =168 days

Expected return on the bill = 4.17 % p.a.

a. Calculation of the amount at which bill has been purchased :

=100,000/1+(0.0417/365 * 168)

= $ 98,116.80

b. Calculation of the amount at which bill would have been purchased when expected return will be 4.81% p.a. :

=100,000/1+(0.0481/365 * 168)

= $97,834.03

c. Calculation of the amount at which bill has been sold by the investor :

= 97,834.03 * 4.81% * 30/365 + 97,834.03

= 386.78 + 97,834.03

= $98,220.81

d. Calculation of the rate of return earned by investor:

=386.78/98,116.80 *100% * 365/30

= 4.796 %