For an investment to double in 5 years, the interest rate has to be 14.11% compounded quarterly.

Question

Quizplus · Accepted Answer

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times per year that the interest is compounded, and t is the number of years. If we want the investment to double in 5 years, then A = 2P. Substituting this into the formula, we get 2P = P(1 + r/n)^(5n). Dividing both sides by P, we get 2 = (1 + r/n)^(5n). Taking the 5th root of both sides, we get 1.1411 = 1 + r/n. Subtracting 1 from both sides, we get 0.1411 = r/n. Multiplying both sides by n, we get 0.1411n = r. Since n = 4 (quarterly compounding), we get 0.1411 * 4 = r = 0.5644, or 14.11% compounded quarterly.

For an Investment to Double in 5 Years, the Interest