Solve the problem.
-If $2500 is invested in an account that pays interest compounded continuously, how long will it take to grow to $5000 at 8%? Round to the nearest tenth.
A) 8.7 years
B) 11.5 years
C) 9.0 years
D) 5.5 years

Question

Quizplus · Accepted Answer

The formula for continuous compounding is $A = Pe^{rt}$, 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), and $t$ is the time the money is invested for in years. We are given $A = 5000$, $P = 2500$, and $r = 0.08$. We need to solve for $t$. Rearranging the formula to solve for $t$, we get $t = \frac{\ln(A/P)}{r}$. Substituting the given values, $t = \frac{\ln(5000/2500)}{0.08} = \frac{\ln(2)}{0.08}$. Calculating this gives $t \approx 8.7$ years.

Solve the Problem. -If $2500 Is Invested in an Account That Pays Interest