How long will it take for $8200 to grow to $42,000 at an interest rate of 4.7% if the interest is compounded continuously? Round the number of years to the nearest hundredth.
A) 34.76 yr
B) 1.11 yr
C) 3475.61 yr
D) 3.48 yr

Question

Quizplus · Accepted Answer

To solve this, 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), 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: $A = 42000$, $P = 8200$, and $r = 0.047$, we find $t = \frac{\ln(42000/8200)}{0.047}$, which calculates to approximately 34.76 years.

How Long Will It Take for $8200 to Grow to $42,000