Gianni invested $10,000 at a rate of 6% compounded annually.How long will it take for the investment to grow to $40,000?
A)1.33 years
B)4.00 years
C)23.79 years
D)50.00 years

Question

Quizplus · Accepted Answer

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. In this case, since the interest is compounded annually, n = 1, P = $10,000, r = 6% or 0.06, and A = $40,000. We need to solve for t. Rearranging the formula to solve for t gives us t = log(A/P) / n[log(1 + r/n)]. Plugging in the values gives us t = log(40,000/10,000) / log(1 + 0.06), which simplifies to t = log(4) / log(1.06). Calculating this gives approximately 23.79 years.

Gianni Invested $10,000 at a Rate of 6% Compounded Annually