Final answer:
To double an investment in 3 years, the interest rate compounded annually required is approximately 0.25992, or 25.992%.
Step-by-step explanation:
To double an investment in 3 years, we need to determine the interest rate compounded annually. Let's assume the initial investment is $1. We can use the compound interest formula:
A = P(1 + r)^t
Where:
- A is the final amount (which is 2 times the initial investment)
- P is the principal amount
- r is the interest rate as a decimal
- t is the number of years
Plugging in the given values, we have:
2 = 1(1 + r)^3
(1 + r)^3 = 2
Now we need to solve for r. Taking the cube root of both sides, we get:
1 + r = ∛∛2
r = ∛∛2 - 1
This value is approximately 0.25992, or 25.992% (option a).