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 5.5%? Round to the nearest tenth.
A) 3.8 years
B) 12.6 years
C) 11.5 years
D) 13.2 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. To find $t$, we rearrange the formula to solve for $t$: $t = \frac{\ln(A/P)}{r}$. Substituting $A = 5000$, $P = 2500$, and $r = 0.055$, we get $t = \frac{\ln(5000/2500)}{0.055} = \frac{\ln(2)}{0.055}$, which calculates to approximately 12.6 years.

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