Problem#3: What is the quarterly compounded rate per annum that is equivalent to 10% per annum...

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Problem#3: What is the quarterly compounded rate per annum that is equivalent to 10% per annum compounded continuously? (a) 1

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Answer 1

Answer #1

Suppose quarterly compounded rate per annum = r

EAR for Quarterly compounding is calculated using the formula:

EAR1 = (1+(r/4))4 - 1

EAR for 10% per annum compounded continuously is calculated using the formula:

EAR2 = e10% - 1 = 1.10517091807565 - 1

It is given that EAR1 = EAR2

(1+(r/4))4 - 1 = 1.10517091807565 - 1

(1+(r/4))4 = 1.10517091807565

1+(r/4) = (1.10517091807565)1/4

1+(r/4) = 1.02531512052443

r/4 = 0.02531512052443

r = 0.02531512052443*4 = 0.101260482097715 = 10.1260482097715% ~ 10.126% (Rounded to three decimal places)

Answer -> 10.126% (option b)

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Answer 2

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