Complete the table for a savings account in which interest is compounded continuously. $$\begin{array} { | c | c | c | c | }
\hline \text { Initial investment } & \text { Annual \% rate } & \text { Time to double } & \text { Amount after 10 years } \
\hline { \$ 750 } & ....& 9 \frac { 3 } { 4 } y r &.... \
\hline
\end{array}$$
(Round the answer up to two decimal places. )
A)Annual rate: $7.11 \%$ Amount after 10 years: $\$ 1527.02$
B)Annual rate: $11.11 \%$ Amount after 10 years: $\$ 1527.02$
C)Annual rate: $7.11 \%$ Amount after 10 years: $\$ 1027.02$
D)Annual rate: $7.11 \%$ Amount after 10 years: $\text { \$2027.02 }$
E)Annual rate: $9.11 \%$ Amount after 10 years: $\$ 1527.02$

Question

Complete the table for a savings account in which interest is compounded continuously. $$\begin{array} { | c | c | c | c | } 
\hline \text { Initial investment } & \text { Annual \% rate } & \text { Time to double } & \text { Amount after 10 years } \
\hline { \$ 750 } & ....& 9 \frac { 3 } { 4 } y r &.... \
\hline
\end{array}$$
(Round the answer up to two decimal places. )
A)Annual rate: $7.11 \%$ Amount after 10 years: $\$ 1527.02$
B)Annual rate: $11.11 \%$ Amount after 10 years: $\$ 1527.02$
C)Annual rate: $7.11 \%$ Amount after 10 years: $\$ 1027.02$
D)Annual rate: $7.11 \%$ Amount after 10 years: $\text { \$2027.02 }$
E)Annual rate: $9.11 \%$ Amount after 10 years: $\$ 1527.02$

Quizplus · Accepted Answer

The formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the amount after time $t$, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (as a decimal), and $e$ is the base of the natural logarithm (approximately 2.71828). To find the annual rate that doubles the investment in $9 \frac{3}{4}$ years, we set $A = 2P$ and solve for $r$. Using the given time to double, $t = 9.75$ years, we get $2 = e^{r \cdot 9.75}$. Solving for $r$ gives approximately $0.0711$ or $7.11\%$. To find the amount after 10 years, we use $A = 750e^{0.0711 \cdot 10}$, which calculates to approximately $\$1527.02$.

Complete the Table for a Savings Account in Which Interest