Solving for Time How many years will it take $200 to grow to $250 with an annual interest rate of 4 percent?
A)1.24 years
B)5.69 years
C)6.25 years
D)18.00 years

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, 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. In this case, we have P = $200, A = $250, r = 4%, n = 1 (since the interest is compounded annually), and we want to solve for t. Plugging these values into the formula, we get 250 = 200(1 + 0.04/1)^(1*t). Dividing both sides by 200, we get 1.25 = (1.04)^t. Taking the logarithm of both sides, we get log(1.25) = t*log(1.04). Dividing both sides by log(1.04), we get t = log(1.25)/log(1.04) = 5.69 years.

Solving for Time How Many Years Will It Take $200