Solve the problem.
-How long will it take for $3000 to grow to $22,600 at an interest rate of 3.1% if the interest is compounded continuously? Round the number of years to the nearest hundredth.
A) 6.51 yr
B) 65.14 yr
C) 0.65 yr
D) 6513.99 yr

Question

Quizplus · Accepted Answer

To solve this problem, we use the formula for continuous compounding interest: $A = Pe^{rt}$, 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), $t$ is the time the money is invested for in years, and $e$ is the base of the natural logarithm, approximately equal to 2.71828. We are given $A = \$22,600$, $P = \$3,000$, and $r = 3.1\% = 0.031$, and we need to solve for $t$. Rearranging the formula to solve for $t$, we get $t = \frac{\ln(A/P)}{r}$. Plugging in the given values: $t = \frac{\ln(22600/3000)}{0.031}$, which calculates to approximately 65.14 years.

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