How many years will it take for $500 to grow to $1,039.50 if invested at 5 percent compounded annually?
A)15
B)14
C)13
D)12

Question

Quizplus · Accepted Answer

The correct answer is A.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 = $500, A = $1,039.50, r = 5%, n = 1 (compounded annually), and we want to find t.Plugging these values into the formula, we get:$1,039.50 = $500(1 + 0.05/1)^(1*t)Dividing both sides by $500, we get:2.079 = (1.05)^tTaking the logarithm of both sides, we get:log(2.079) = t*log(1.05)Dividing both sides by log(1.05), we get:t = log(2.079)/log(1.05)Evaluating this expression, we get:t = 14.999...Since we can't have a fraction of a year, we round up to the nearest whole number, which is 15.Therefore, it will take 15 years for $500 to grow to $1,039.50 if invested at 5 percent compounded annually.

How Many Years Will It Take for $500 to Grow