Question
Question 10
Suppose money invested in a hedge fund earns 1% per trading day. There are 250 trading days per year. With an initial investment of $100, what will be your annual return assuming the manager puts all of your daily earnings into a zero-interest-bearing checking account and pays you everything earned at the end of the year?
*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. With an initial investment of $100, what will be your annual return assuming the manager puts all of your daily earnings into a zero-interest-bearing checking account and pays you everything earned at the end of the year?
*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 an investment earning 1% per trading day, we can use the formula for compound interest:
\[ A = P \times (1 + r)^n \]
where:
- \( A \) is the amount of money accumulated after n days, including interest.
- \( P \) is the principal amount (initial investment).
- \( r \) is the daily interest rate (1% or 0.01).
- \( n \) is the number of trading days in a year (250).
Given:
- \( P = 100 \)
- \( r = 0.01 \)
- \( n = 250 \)
Plugging these values into the formula:
\[ A = 100 \times (1 + 0.01)^{250} \]
Calculating \( (1 + 0.01)^{250} \):
\[ (1 + 0.01)^{250} = (1.01)^{250} \]
Now we can compute this value:
Using logarithms or a calculator:
\[ (1.01)^{250} \approx 9.646 \]
Now plug this back into the formula for total amount:
\[ A \approx 100 \times 9.646 = 964.63 \]
Now, the annual return, which is the total amount after one year minus the initial investment:
\[ \text{Annual Return} = A - P = 964.63 - 100 = 864.63 \]
Therefore, the annual return, to two decimal places, is:
**864.63**
\[ A = P \times (1 + r)^n \]
where:
- \( A \) is the amount of money accumulated after n days, including interest.
- \( P \) is the principal amount (initial investment).
- \( r \) is the daily interest rate (1% or 0.01).
- \( n \) is the number of trading days in a year (250).
Given:
- \( P = 100 \)
- \( r = 0.01 \)
- \( n = 250 \)
Plugging these values into the formula:
\[ A = 100 \times (1 + 0.01)^{250} \]
Calculating \( (1 + 0.01)^{250} \):
\[ (1 + 0.01)^{250} = (1.01)^{250} \]
Now we can compute this value:
Using logarithms or a calculator:
\[ (1.01)^{250} \approx 9.646 \]
Now plug this back into the formula for total amount:
\[ A \approx 100 \times 9.646 = 964.63 \]
Now, the annual return, which is the total amount after one year minus the initial investment:
\[ \text{Annual Return} = A - P = 964.63 - 100 = 864.63 \]
Therefore, the annual return, to two decimal places, is:
**864.63**