
Question 9

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.*

To calculate the annual return on an investment where you earn 1% per trading day and reinvest the earnings, we can use the formula for compound interest. The formula is:

\[
A = P \times \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the amount of money accumulated after $ t $ years, including interest.
- $ P $ is the principal amount (initial investment).
- $ r $ is the annual interest rate (as a decimal).
- $ n $ is the number of times that interest is compounded per year.
- $ t $ is the time the money is invested for, in years.

### Step 1: Identify the Variables
Given:
- $ P = 100 $ (initial investment)
- $ r = 1\% $ per trading day, so $ r_{\text{daily}} = 0.01 $
- $ n = 250 $ trading days per year
- $ t = 1 $ year

### Step 2: Calculate the Annual Return
We need to calculate the amount $ A $ after 1 year:

\[
A = 100 \times \left(1 + 0.01\right)^{250}
\]

### Step 3: Compute the Final Value
Now let's compute the value:

\[
A = 100 \times (1.01)^{250}
\]

Calculating $ (1.01)^{250} $:

\[
A = 100 \times 12.031 \approx 1203.28
\]

### Step 4: Determine the Annual Return
The annual return is the final amount minus the initial investment:

\[
\text{Annual Return} = 1203.28 - 100 = 1103.28
\]

### Final Answer:
The annual return on $100 invested in the fund is **1103.28**.

Would you like more details on the steps? Here are some related questions for further exploration:

1. How would the annual return change if the daily return was 0.5%?
2. What if the trading days per year were reduced to 200?
3. How does the daily compounding frequency affect the final return compared to monthly compounding?
4. Can you calculate the final value after 2 years with the same daily return?
5. What if the investment allowed quarterly withdrawals instead of reinvestment?

**Tip:** Daily compounding can significantly increase your returns over time, especially when the interest rate per period is high.

Learn how to calculate the annual return on an investment with daily compound interest. Given an initial investment of $100 earning 1% per trading day reinvested daily, find out the final amount after one year. Explore the compound interest formula and detailed steps to compute the return. Suitable for Grades 10-12.

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