Question
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.
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.
Answers
GPT-4o mini
To calculate the annual return on $100 invested in a hedge fund that earns 1% per trading day with daily compounding for 250 trading days, we can use the formula for compound interest:
\[
A = P(1 + r)^n
\]
Where:
- \( A \) is the amount of money accumulated after n days, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the daily interest rate (1% in this case, which is 0.01).
- \( n \) is the number of trading days (250 in this case).
Plugging in the values:
\[
A = 100(1 + 0.01)^{250}
\]
Calculating \( (1 + 0.01)^{250} \):
\[
(1 + 0.01)^{250} = (1.01)^{250}
\]
Using a calculator or computation tool to find \( (1.01)^{250} \):
\[
(1.01)^{250} \approx 9.64629
\]
Now, we can calculate \( A \):
\[
A = 100 \times 9.64629 \approx 964.63
\]
Finally, to find the annual return, subtract the principal from the total amount:
\[
\text{Annual Return} = A - P = 964.63 - 100 = 864.63
\]
Thus, the annual return on the investment is:
\[
\boxed{864.63}
\]
\[
A = P(1 + r)^n
\]
Where:
- \( A \) is the amount of money accumulated after n days, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the daily interest rate (1% in this case, which is 0.01).
- \( n \) is the number of trading days (250 in this case).
Plugging in the values:
\[
A = 100(1 + 0.01)^{250}
\]
Calculating \( (1 + 0.01)^{250} \):
\[
(1 + 0.01)^{250} = (1.01)^{250}
\]
Using a calculator or computation tool to find \( (1.01)^{250} \):
\[
(1.01)^{250} \approx 9.64629
\]
Now, we can calculate \( A \):
\[
A = 100 \times 9.64629 \approx 964.63
\]
Finally, to find the annual return, subtract the principal from the total amount:
\[
\text{Annual Return} = A - P = 964.63 - 100 = 864.63
\]
Thus, the annual return on the investment is:
\[
\boxed{864.63}
\]