An investor in a mutual fund earns a 25% return the first year, loses 25% in the second year, gains 30% in the third year, and then loses 30% in the fourth year. The average annual compound growth rate of this investment and the value of an initial $10,000 investment at the end of four years are closest to: Compound Growth Ending Value a. -3.9% 8,530 b. 0% 8,530 c. 0% 10,000 d. -3.9% 10,000
(1.25*.75*1.30*.70)^.25=.9611 .9611-1=-.03893 -3.893% annualized rate of return A You can eliminate B and C right off the bat. They want you to add the returns together which would be incorrect. If you’re annualized return is -3.9% there is no way that you will still have your original principal. So that would eliminate D as well.
A
Thanks a lot guys! This really helped!
Chuckrox8 Wrote: ------------------------------------------------------- > (1.25*.75*1.30*.70)^.25=.9611 > > .9611-1=-.03893 -3.893% annualized rate of > return > > A > > > You can eliminate B and C right off the bat. They > want you to add the returns together which would > be incorrect. If you’re annualized return is > -3.9% there is no way that you will still have > your original principal. So that would eliminate > D as well. whats the logic for raising to the 25% power?
The question asks for the “annualized” compound rate of growth/return. If you compute (1.25*.75*1.30*.70)=.8531 .8531-1=-14.68% you have only solved for the total return. You still need to find the annualized geometric mean. Over a 4 year period I know that Yr1*Yr2*Yr3*Yr4=.8531, How do I convert this into an annualized number? Simply take .8531 and raise it to ^(1/n years) .8531^(1/4) or (.25 as I did) =.96105 and subtract 1 to get your final answer of -3.9%.
Yeah, this is basically the geometric mean of the returns.