Final answer:
To find the interest rate when money doubles in 7 years with annual compounding, we can use the compound interest formula and solve for the rate. By plugging in the given values and simplifying the equation, we find that the interest rate is approximately 10.9%.
Step-by-step explanation:
To calculate the interest rate, we can use the formula for compound interest: A = P(1+r/n)^(nt), where A is the future value, P is the initial principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
- Let's assume the initial principal amount is $100.
- Since the money doubled in 7 years, the future value (A) is $200.
- Plugging in the values into the formula, we have: $200 = $100(1+r/1)^(1*7).
- Simplifying the equation, we get: 2 = (1+r)^7.
- To solve for r, we need to isolate it. Taking the seventh root of both sides, we get: (1+r) = 2^(1/7).
- Subtract 1 from both sides: r = 2^(1/7) - 1.
- Using a calculator, we can find that r ≈ 0.109.
Therefore, the interest rate received, when compounded annually, is approximately 10.9%.