Solve the problem.
-How long will it take for $3600 to grow to $7300 at an interest rate of 2.8% if the interest is compounded continuously? Round the number of years to the nearest hundredth.
A) 2524.79 yr
B) 25.25 yr
C) 0.55 yr
D) 2.52 yr

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 or borrowed for, in years. Rearranging the formula to solve for $t$, we get $t = \frac{\ln(A/P)}{r}$. Substituting $A = 7300$, $P = 3600$, and $r = 0.028$, we find $t = \frac{\ln(7300/3600)}{0.028}$, which calculates to approximately 25.25 years.

Solve the Problem. -How Long Will It Take for $3600 to Grow to to Grow