Final answer:
The annual interest rate for the investment is approximately 5.96%, calculated using the compound interest formula based on the known initial deposit, final balance, and compounding frequency.
Step-by-step explanation:
To calculate the annual interest rate of a long-term investment fund with quarterly compounding and a known final balance, we use the formula for compound interest, which is A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
We are given:
- P = $2000
- A = $2759.31
- n = 4 (since interest is compounded quarterly)
- t = 6 years
Solving for r in the compound interest formula, and calculating using the given values, we find that the annual interest rate is approximately 5.96%.