Question #191264

XYZ funds purchased a bank bill (face value=1 million) on 10th June 2020. The bill will mature in 60 days and the yield is 6.95%. After holding the bill for 40 days, the funds sold the bill at a yield of 6.5%.

a) Calculate the profit through buy and sell of this bank bill. (4.5 marks)

b) Work out the simple annual interest rate and effective annual interest rate earned by XYZ.(4 marks)

Expert's answer

a).

First, purchase price will be calculated.

Face value = 1,000,000

Yield rate = 6.95%

Time = 60 days

"Face\\space value=1,000,000"

"Discounted\\space amount=1,000,000\\times9.65\\%\\times\\frac{60}{365}"

"=11,424.66"

"Purchase\\space price=Face\\space value-Discounted\\space amount"

"=1,000,000-11,424.66"

"=988,575.37"

"Time=20\\space days(60-40)"

"Yield\\space on\\space sale=6.5\\%"

"Sale\\space price=1,000,000-(1,000,000\\times 6.5\\%\\times\\frac{20}{365})"

"=1,000,000-3,561.64"

"=996,438.36"

"Profit\\space earned=Sale\\space price-Purchase\\space price"

"=996,438.36-988,575.34"

"=7,863.02"

Hence profit is "7,863.02"

(b)

Computation of interest:-

"\\frac{Simple\\space interest}{Profit}=Amount\\space invested\\times Rate\\times Time"

"7,863.02=988,575.34\\times Rate \\times\\frac{40}{365}"

"7,863.02=108,337.02\\times Rate"

"Rate=\\frac{7,863.02}{108,337.02}"

"=0.07258\\space or\\space 7.158\\%"

"Effective\\space annual\\space interest\\space rate(EAR)"

"=(1+\\frac{Rate}{compound\\space period})^{compounding\\space period}-1"

"=(1+\\frac{0.07258}{365})^{365}-1"

"=(1+0.000199)^{365}-1"

"=1.07533-1"

"=0.07533\\space or\\space 7.533\\%"

Simple interest is 7.158% and EAR is 7.533%

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