Question

1. An interest rate is 5% per annum with continuous compounding. What is the equivalent rate with semiannual compounding?

Answer 1

Effective annual rate with continous compounding = e^rt - 1

r = rate of interest = 5% or 0.05

t = time in years = 1

= e^0.05 - 1 = 1.05127 - 1 = 0.05127 or 5.127 %

Effective annual rate with semi annual compounding is given by .............

( 1 + r/2 )² - 1 = 0.05127  

( 1 + r/2 )² = 1.05127

(1 + r/2) = squre root of ( 1.05127) = 1.02531

r/2 = 0.02531

r = 0.05062 or 5.062 % ..............final answer.

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