Question

Jenna decides to purchase a U.S. Treasury Bill for 95,000. The Treasury Bill matures in 180 days for 100,000. Let QR be the quoted rate on this U.S. Treasury Bill. Let j be the annual effective yield on this U.S. Treasury Bill assuming a 365 day year. Calculate j−QR.

Answer 1

Answer:

J-QR =0.96

Explanation:

Quoted interest rate(QR) is nominal interest rate that does not take compounding into consideration

Effective interest rate(J) is real interest rate that accounts for compounding

face value of tbill = 100,000

price = 95,000

time remaining for maturity, n = 180

QR T-Bill = [(Face Value - Price)/(Face Value)] *(360/n) = [(100,000-95,000)/100,000]*(360/180) = (5000/100,000)*2 = 0.10 or 10%

j = (1+ ((Face Value - Price)/price))(365/n) -1 = (1+((100,000-95,000)/95,000))(365/180) -1 = (1+(5000/95000))2.027778 -1 = 0.1096131

j = 0.1096131 or 10.96131% or 10.96%

Therefore j-QR = 10.96-10 = 0.96%