A company invests its surplus funds by buying a commercial bill with a face value of $100 000,at a current yield to maturity of 7.35% per annum and 120 days to maturity.After 45 days,the bill is sold at a yield of 6.84% per annum.What rate of return did the company earn on the bill?
A) 4.85% per annum
B) 8.01% per annum
C) 8.09% per annum
D) 8.90% per annum

Question

Quizplus · Accepted Answer

First, we need to calculate the price of the bill when it was bought:
PV = FV / (1 + r * t/365)
where PV is the present value, FV is the face value, r is the yield to maturity, and t is the time to maturity.
PV = 100000 / (1 + 0.0735 * 120/365) = 98661.97
After 45 days, the remaining time to maturity is 75 days, and the new yield to maturity is 0.0684.
So, the selling price of the bill is:
Selling price = PV * (1 + r * t/365)
Selling price = 98661.97 * (1 + 0.0684 * 75/365) = 99294.46
The gain on the bill is:
Gain = Selling price - PV = 99294.46 - 98661.97 = 632.49
The rate of return on the bill is:
Rate of return = Gain / PV * (365 / t)
Rate of return = 632.49 / 98661.97 * (365 / 120) = 0.0809 or 8.09% per annum.

A Company Invests Its Surplus Funds by Buying a Commercial