Question

Which of the following provides the greatest annual return? 16% compounded quarterly 15% compounded continuously 16% compounded annually all of these are exactly equal 15.2% compounded daily

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Answer 1

Calculating Effective Annual Rate(EAR) for each of the option to determine the greatest annual return:-

i) 16% compounded Quarterly

EAR = (1+-)" - 1 m

where, r = Interest rate = 16%

m = No of times compounding in a year = 4

$EAR = (1+\frac{0.16}{4})^4-1$

EAR = 1.169859 - 1

EAR = 16.9859%

ii) 15% compounded continously

EAR=e" - -1

where, r = Interest rate = 15%

EAR = 1.161834 - 1

EAR = 16.1834%

iii) 16% compounded annually

EAR = (1+-)" - 1 m

where, r = Interest rate = 16%

m = No of times compounding in a year = 1

$EAR =(1+\frac{0.16}{1})^1-1$

EAR = 1.16 - 1

EAR = 16%

iv) 15.20% compounded Daily

EAR = (1+-)" - 1 m

where, r = Interest rate = 15.20%

m = No of times compounding in a year = 365

$EAR =(1+\frac{0.1520}{365})^{365}-1$

EAR = 1.164123 - 1

EAR = 16.4123%

As EAR of 16% componded Quarterly is highest among the other Options, it is better to choose "16% Compounded Quarterly".

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