Question

Steven purchased 1000 shares of a certain stock for $27,400 (including commissions). He sold the shares 3 years later and received $34,500 after deducting commissions. Find the effective annual rate of return on his investment over the 3-year period.

(Round your answer to two decimal places.)
%/year

Answer 1

Answer-

Number of shares purchased = 1000
Total amount including commissions = $ 27400

The amount received after sale deducting commissions = $ 34500

The effective annual rate of return over 3 year period is calculated as

Compounded annual growth rate ( CAGR ) = ( Ending investment rate / Sarting amount )1 /n - 1

n = Number of years = 3 years

CAGR = ( $ 34500 / $ 27400 ) (1/3) - 1
CAGR = (1.259)(1/3)  - 1
CAGR = 1.259(0.333) - 1
CAGR = 1.07971 - 1
CAGR = 0.07971
CAGR = 7.97 %  

The effective annual rate of return is the real return on a account or any interest-paying investment when the effects of compounding over time are taken into consideration which is the CAGR. Here the amount is compounded annually and hence the annual rate / year is calculated.

Here the Effective annual rate of return = CAGR = 7.97 % / year.