Question

An investor made a $3000 investment. In the first year, she earned a rate of return of 40% on her investment. In her second year, she lost 10% on her investment. At the end of her second year, her investment was worth ______ Her true annual average rate of return (% to 2 decimal places) over this 2-year period was ______

Answer 1

after first year :

total = $3000*(1+return)

= $3000*(1 + 40%)

= $3000*(1 + 0.40)

= $4200

after second year :

total = (total after 1st year)*(1 + return)

= $4200 * (1 + (-10%))

= $4200 * (1 + (-0.10))

= $ 3780

therefore at the end of second year, total worth of investment = $3780

true annual average rate of return = [ (investment worth after 2 years - investment) / (investment) ]*100% * (1/no. of years)

= [ (3780-3000)/3000 ]*100 % * (1/2)

= 26% * (1/2)

= 13%

true annual average rate of return is 13%

(PLEASE UPVOTE)