Suppose money invested in a hedge fund earns 1% per trading day. There are 250 trading days per year. What will be your annual return on $100 invested in the fund if the manager allows you to reinvest in the fund the 1% you earn each day?
100 * 1.01^250
To calculate the annual return on $100 invested in the hedge fund, we need to take into account the compounding effect of reinvesting the 1% earned each trading day.
First, let's calculate the amount of money you would have at the end of each trading day:
Day 1: $100 + 1% = $100 + $1 = $101
Day 2: $101 + 1% = $101 + $1.01 = $102.01
Day 3: $102.01 + 1% = $102.01 + $1.02 = $103.03
...
Day 250: $XXX.XX
Now, let's calculate the final amount at the end of the year by compounding the daily returns:
Final amount = $100 * (1 + 0.01)^250
Using the compound interest formula, we can calculate the final amount:
Final amount = $100 * (1.01)^250
Calculating this in a calculator or spreadsheet, the final amount would be approximately $434.04.
Therefore, your annual return on $100 invested in the hedge fund, with reinvestment, would be $434.04 - $100 = $334.04.
To calculate the annual return on $100 invested in the hedge fund, with the option to reinvest the 1% earned each trading day, we need to use compound interest formula.
First, let's calculate the daily return. A 1% return each trading day means the investment grows by 0.01 (1%) every day.
Next, let's calculate the number of trading days in a year. Given that there are 250 trading days per year, we'll use this as the number of compounding periods.
Now, let's plug these values into the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = final amount (the total return)
P = principal (initial investment)
r = interest rate per compounding period (daily return)
n = number of compounding periods per year (trading days)
t = number of years
In this case:
P = $100
r = 0.01 (1% daily return)
n = 250 (number of trading days per year)
t = 1 (since we're calculating the annual return)
Let's calculate:
A = 100(1 + 0.01/250)^(250*1)
= 100(1 + 0.00004)^250
= 100(1.00004)^250
≈ 100(1.01005)
≈ $101.01
Therefore, the annual return on $100 invested in the hedge fund, with the option to reinvest the 1% earned each day, would be approximately $101.01.