Question

Suppose that you open a mutual fund account with a deposit of $540.
5 months later, the fund balance is $610, and you withdraw $192. A year after the account was opened, your balance is $. If the dollar-weighted and time-weighted yield rates were the same, what is the rate of return?

Answer 1

Sol:

Initial deposits = $540 (for 5 months)

Balance after 5 months = $610 - $192 = $418 (for 7 months)

Total weighted amount = $540 x 5/12 and $418 x 7/12

Total weighted amount = $225 and $243.83

Total weighted amount = $225 + $243.83 = $468.83

Therefore balance a year after the account was opened will be $468.83

To determine weighted rate of return is as follows,

Initial deposits = $540 (for first 5 months earnings = 100)

Balance after 5 months = $418 (for 7 months) = 418 x 100/540 = 77.4074

Now earnings for next 7 months will be = 77.4074 x 7/5 = 108.3704

Total 12 months earnings = 5 month earnings + 7 month earnings

Total 12 months earnings = 100 + 108.3704 = 208.3704

Weighted rate of return = Total 12 months earnings / Total weighted amount x 100

Weighted rate of return = 208.3704/468.83 x 100

Weighted rate of return = 44.44%

Therefore rate of return will be 44.44%