Question

Ninety days ago, Elena bought in a 180-day bank-accepted bill yielding 9 per cent per annum. Calculate the return that he will earn if the bill is sold today, given that 90-day bills are currently yielding 7 per cent per annum in the market.
A. 10.81%
B. 9%
C. 7%
D. Cannot be determined based on the given information

Answer: A

Q: Can you show t calculation ???

Answer 1

Let Face value of bank accepted bill = $1000

First we will calculate the price of bank accepted bill 90 days ago

Days to maturity = 180, Yield = r = 9% per annum

Face value = Price of bank accepted bill 90 days ago x [1 + r(days to maturity/360)]

1000 = Price of bank accepted bill 90 days ago x [1 + 9%(180/360)]

1000 = Price of bank accepted bill 90 days ago x [1 + 9%(1/2)]

1000 = Price of bank accepted bill 90 days ago x [ 1+4.5%]

Price of Bank accepted bill 90 days ago = 1000 / [1+4.5%] = 1000 / 1.045 = $956.9377

Now we will calculate current price of Bank accepted bill

Days to maturity = 90 days , Yield = r = 7%

Face value = Current Price x [1 + r(days to maturity/360)]

1000 = Current Price x [1 + 7%(90/360)]

1000 = Current Price x [ 1+ 7%(1/4)]

1000 = Current Price x [ 1 + 1.75%]

Current Price = 1000 / [ 1 + 1.75%] = 1000 / 1.0175 = 982.8009

Holding period = 90 days

Return earned = [(Current Price / Price of bank accepted bill 90 days ago) - 1 ][360/Holding period]

Return earned = [(982.8009 / 956.9377) - 1 ][360 / 90] = [1.027027 - 1][4] = 0.027027 x 4 = 2.7027% x 4 = 10.8108% = 10.81% (rounded to two decimal places)

Hence Return earned if bill is sold today = 10.81%

Answer A. 10.81%