How many years will it take $100 to grow to $1,000 with an annual interest rate of 8 percent?
A) 9.00 years
B) 10.00 years
C) 29.92 years
D) 33.35 years

Question

Quizplus · Accepted Answer

To find the number of years it takes for an investment to grow from $100 to $1,000 with an annual interest rate of 8 percent, we can use the formula for compound interest: $A = P(1 + r)^t$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount ($100), $r$ is the annual interest rate (8% or 0.08), and $t$ is the time the money is invested for in years. Rearranging the formula to solve for $t$, we get $t = \frac{\log(A/P)}{\log(1 + r)}$. Plugging in the values, $t = \frac{\log(1000/100)}{\log(1 + 0.08)} = \frac{\log(10)}{\log(1.08)} \approx 29.92$ years.

How Many Years Will It Take $100 to Grow to $1,000