Question

(1 pt) Suppose that you open a mutual fund account with a deposit of 505 dollars. 5 months later, the fund balance is 595 dollars, and you withdraw 192 dollars. A year after the account was opened, your balance is X dollars. If the dollar weighted and time weighted rates of return were the same, what is the rate of return? (Assume simple interest for the dollar weighted calculation.) Answer = percent.

Can use excel as long as answer is correct

Answer 1

For the first 5 months, Holding period return HPY1= (595-505)/505 = 90/505 = 0.178218

For the second period of 7 months , Holding period return HPY2= (X-(595-192))/(595-192) =(X-403)/403

Time weighted return for the whole year = (1+HPY1)*(1+HPY) -1 = 1.178218*X/403 -1 =0.002924*X -1

Dollar weighted return (r) is given by the equation

-505+192/(1+r*5/12)+X/(1+r) = 0

As both Time weighted and Dollar weighted returns are same we get

-505 + 192/(0.002924*X*5/12+7/12) + X/(0.002924*X) = 0

192/(0.002924*X*5/12+7/12) = 162.958

(0.002924*X*5/12+7/12) = 1.178218

0.001218*X = 0.594884

X = 488.34

So the value of X is $488.34

and the rate of return = 0.002924*488.34-1 = 0.4277 = 42.77%