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?
*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.
1 point
To calculate the annual return on $100 invested in the fund with daily reinvestment, we need to calculate the cumulative return after 250 trading days.
For each trading day, the investment grows by 1%, so the amount after each day can be calculated as:
Day 1: $100 * (1 + 0.01) = $101
Day 2: $101 * (1 + 0.01) = $102.01
Day 3: $102.01 * (1 + 0.01) = $103.03
...
Day 250: $100 * (1 + 0.01)^250
To calculate the annual return, we need to subtract the initial investment of $100 from the final amount after 250 trading days and then divide it by the initial investment, and then multiply by 100 to express it as a percentage.
Final amount after 250 trading days = $100 * (1 + 0.01)^250
Annual return on $100 = (($100 * (1 + 0.01)^250) - $100) / $100 * 100
Calculating this expression will give us the annual return on the $100 invested in the hedge fund with daily reinvestment of the 1% earned each day.