Compute the compound interest.
-How long will it take for $\$ 7700$ to grow to $\$ 27,200$ at an interest rate of $10.9 \%$ if the interest is compounded continuously? Round the number of years to the nearest hundredth.
A) $10.9 \mathrm{yr}$
B) $1157.8 \mathrm{yr}$
C) $11.58 \mathrm{yr}$
D) $1.16 \mathrm{yr}$

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 (\$7700), $r$ is the annual interest rate (10.9% or 0.109 as a 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 the given values, $t = \frac{\ln(27200/7700)}{0.109}$, which calculates to approximately 11.58 years.

Compute the Compound Interest $7700\$ 7700$7700 To Grow To $27,200\$ 27,200$27,200 At an Interest Rate Of

Compute the Compound Interest $\$ 7700$ To Grow To $\$ 27,200$ At an Interest Rate Of