Complete the table for a savings account in which interest is compounded continuously.$$\begin{array} { | c | c | c | c | }
\hline \text { Initial investment } & \text { Annual } \% \text { rate } & \text { Time to double } & \text { Amount after 10 years } \
\hline { \$ 500 } & 9 \frac { 1 } { 2 } \% & ....& .....\\
\hline
\end{array}$$
(Round the answer up to two decimal places. )
A)Time to double: $7.30 y r$ Amount after 10 years: $\$ 1292.85$
B)Time to double: $7.30 y r$ Amount after 10 years: $\$ 1542.85$
C)Time to double: $2.30 y r$ Amount after 10 years: $\$ 1292.85$
D)Time to double: $7.30 y r$ Amount after 10 years: $\$ 1792.85$
E)Time to double: $12.30 \mathrm { yr }$ Amount after 10 years: $\$ 1292.85$

Question

Complete the table for a savings account in which interest is compounded continuously.$$\begin{array} { | c | c | c | c | } 
\hline \text { Initial investment } & \text { Annual } \% \text { rate } & \text { Time to double } & \text { Amount after 10 years } \
\hline  { \$ 500 } & 9 \frac { 1 } { 2 } \% & ....& .....\\
\hline
\end{array}$$
(Round the answer up to two decimal places. )
A)Time to double: $7.30 y r$ Amount after 10 years: $\$ 1292.85$
B)Time to double: $7.30 y r$ Amount after 10 years: $\$ 1542.85$
C)Time to double: $2.30 y r$ Amount after 10 years: $\$ 1292.85$
D)Time to double: $7.30 y r$ Amount after 10 years: $\$ 1792.85$
E)Time to double: $12.30 \mathrm { yr }$ Amount after 10 years: $\$ 1292.85$

Quizplus · Accepted Answer

The formula for continuous compounding is $A = P e^{rt}$, where $A$ is the amount after time $t$, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal form), and $e$ is the base of the natural logarithm (approximately 2.71828). To find the time to double, set $A = 2P$ and solve for $t$. Using $r = 9.5\% = 0.095$, the equation becomes $2 = e^{0.095t}$. Solving for $t$ gives approximately $7.30$ years. To find the amount after 10 years, use the formula with $t = 10$, which gives $A = 500e^{0.095 \times 10}$, resulting in approximately $\$1292.85$.

Complete the Table for a Savings Account in Which Interest