Answer to Question #191264 in Finance for Animesh Gautam

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)


1
Expert's answer
2021-05-11T14:16:00-0400

a).

First, purchase price will be calculated.

Face value = 1,000,000

Yield rate = 6.95%

Time = 60 days

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

Discounted amount=1,000,000×9.65%×60365Discounted\space amount=1,000,000\times9.65\%\times\frac{60}{365}

=11,424.66=11,424.66

Purchase price=Face valueDiscounted amountPurchase\space price=Face\space value-Discounted\space amount

=1,000,00011,424.66=1,000,000-11,424.66

=988,575.37=988,575.37


Time=20 days(6040)Time=20\space days(60-40)

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

Sale price=1,000,000(1,000,000×6.5%×20365)Sale\space price=1,000,000-(1,000,000\times 6.5\%\times\frac{20}{365})

=1,000,0003,561.64=1,000,000-3,561.64

=996,438.36=996,438.36


Profit earned=Sale pricePurchase priceProfit\space earned=Sale\space price-Purchase\space price

=996,438.36988,575.34=996,438.36-988,575.34

=7,863.02=7,863.02


Hence profit is 7,863.027,863.02


(b)

Computation of interest:-

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

7,863.02=988,575.34×Rate×403657,863.02=988,575.34\times Rate \times\frac{40}{365}

7,863.02=108,337.02×Rate7,863.02=108,337.02\times Rate

Rate=7,863.02108,337.02Rate=\frac{7,863.02}{108,337.02}

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

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


=(1+Ratecompound period)compounding period1=(1+\frac{Rate}{compound\space period})^{compounding\space period}-1


=(1+0.07258365)3651=(1+\frac{0.07258}{365})^{365}-1


=(1+0.000199)3651=(1+0.000199)^{365}-1



=1.075331=1.07533-1


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


Simple interest is 7.158% and EAR is 7.533%


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