Suppose that you open a mutual fund account with a deposit of 500 dollars. 5 months later, the fund balance is 600 dollars, and you withdraw 216 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

The question is not complete, below is the complete question:

Suppose that you open a mutual fund account with a deposit of 500 dollars. 5 months later, the fund balance is 600 dollars, and you withdraw 216 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 should be a percent!!!

The rate of return is 48% on deposited fund.

Explanation:

The rate of return on investment is the percentage increase on an amount invested for a particular period of time, and to calculate this, we will use the simple interest formula:

I = P × R × T

Where:

P = principal = $500

R = rate in decimal ( %rate/100)

T = time = 5 months = 5/12 years

I = interest = Principal - final balance = 600 - 500 = $100

∴ 100 = 500 × R/100 × 5/12

100 =

120,000 = 2500R

∴ R = 120,000 ÷ 2500 = 48%

Therefore rate of return (R) = 48%

For a clearer understanding of the concept of interests, let us calculate for the balance after one year (X) as shown below:

I = P×R×T

T = 1 because, X is the balance after one year.

I = 500 × 48/100 × 1

I = $240

therefore the final amount after one year = interest + principal

= 240 + 500 = 740

but we were told that $216 was withdrawn at 5 months, hence the balance after one year = 740 - 216 = $524

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