Solve the problem.
-How long will it take for $5100 to grow to $5300 at an interest rate of 4.4% if the interest is compounded continuously? Round the number of years to the nearest hundredth.
A) 0.87 yr
B) 0.09 yr
C) 87.42 yr
D) 0.03 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 $t = \frac{\ln(A/P)}{r}$. Plugging in the given values: $A = 5300$, $P = 5100$, and $r = 0.044$, we get $t = \frac{\ln(5300/5100)}{0.044}$, which approximately equals 0.87 years.

Solve the Problem. -How Long Will It Take for $5100 to Grow to to Grow