An investment of $1250 is made in an account that compounds interest continuously. After years 10 the balance in the account is $2,040.40. To the nearest tenth of a percent, what is the annual interest rate for this account?
A) $6.3 \%$
B) $10.7 \%$
C) $4.9 \%$
D) $0.5 \%$
E) $2.1 \%$

Question

Quizplus · Accepted Answer

The formula for continuous compounding is $A=P e^{rt}$ where $A$ is the ending balance, $P$ is the principal, $r$ is the annual interest rate in decimal form, and $t$ is the time in years.

Plugging in the given values, we get $2040.40=1250 e^{10r}$. Solving for $r$, we get $r\approx 0.04915$. Converting to a percentage, we get $\boxed{	extbf{(C)}\ 4.9\%}$.

An Investment of $1250 Is Made in an Account That 6.3%6.3 \%6.3%

An Investment of $1250 Is Made in an Account That $6.3 \%$