Solve the problem.
-How long will it take for $3000 to grow to $38,800 at an interest rate of 6.2% if the interest is compounded continuously? Round the number of years to the nearest hundredth.
A)41.29 yr
B)0.41 yr
C)4128.72 yr
D)4.13 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 for in years. Rearranging the formula to solve for $t$, we get $t = \frac{\ln(A/P)}{r}$. Substituting $A = 38800$, $P = 3000$, and $r = 0.062$ into the formula gives $t = \frac{\ln(38800/3000)}{0.062}$, which calculates to approximately 41.29 years.

Solve the Problem. -How Long Will It Take for $3000 to Grow to to Grow