Solve.
-How long will it take for $8600 to grow to $35,700 at an interest rate of 7.1% if the interest is compounded continuously? Round the number of years to the nearest hundredth.
A) 20.05 yr
B) 2.00 yr
C) 2 yr
D) 2004.77 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. To find $t$, we rearrange the formula to $t = \frac{\ln(A/P)}{r}$. Substituting the given values, $A = 35700$, $P = 8600$, and $r = 0.071$, we get $t = \frac{\ln(35700/8600)}{0.071}$, which calculates to approximately 20.05 years.

Solve. -How Long Will It Take for $8600 to Grow to to $35,700