Final answer:
To triple an investment in 27 years, the required rate of interest compounded annually is approximately 7.25%.
Step-by-step explanation:
To triple an investment in 27 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future value, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, we want to find the rate of interest compounded annually, so n = 1.
Let's assume the principal amount is P. Given that we want to triple the investment, the future value A will be 3 times the principal amount: 3P. We also know the number of years is 27, so t = 27.
Plugging these values into the formula, we have: 3P = P(1 + r/1)^(1*27). Simplifying, we get: 3 = (1 + r)^27. To solve for r, we can take the 27th root of both sides: (1 + r) = 3^(1/27). Subtracting 1 from both sides, we get: r = 3^(1/27) - 1. Using a calculator, we find that r is approximately 0.072480625, or 7.25%.