Question

Marwan bought a 13-week, $5000 face value Treasury bill to yield 5%. After 50 Days, he sold the T-bill to Ahmed who wishes to yield 4.5%. What rate of return did Marwan earn on his investment?

Answer 1

Number of days in 13 weeks, n = 13 * 7 = 91

r = 0.05/365 = 0.0001369863014 per day

The purchase price is:

Price = FV/(1 + r)^n

Price = 5,000/(1 + 0.0001369863014)^91

Price = $4,938.0623269626

Selling price with n = (91 - 50) = 41

r = 4.5%/365 = 0.0001232876712

Selling price = 5,000/(1 + 0.0001232876712)^41

Selling price = $4,974.791347282

Rate of return = Selling price/Purchase price - 1

Rate of return = 4,974.791347282/4,938.0623269626 - 1

Rate of return = 0.007437941826 (This is the holding period return for 50 days)

Rate of return = 0.007437941826 * 365/50

Rate of return = 0.05429697533

Rate of return = 5.429697533% Per year