Question

Suppose you invest $\$800$ into an annuity account that pays $7.2\%$ annual interest, compounded continuously.

How much will you have in the account in $10$ years?

• A. $\$1,643.55$
• B. $\$1,633.06$
• C. $\$1,693.60$
• D. $\$1,603.39$

Answer 1

The correct option is A

$\$1,643.55$

Explanation for the correct option:

We know that,

Interest formula for the compounded continuously

$A=P{e}^{rt}$

Where

$A$ is final value

$P$ is original principal sum

$r$ is annual rate of interest

$t$ is time period

Given,

$P=\$800$. $r=7.2\%$, $t=10$

$$\begin{gathered} \Rightarrow A=800\times e^{\frac{7.2}{100}\times 10} \\ =800\times e^{0.72} \\ =800\times 2.0544 \\ =1643.55 \end{gathered}$$

Therefore, after $10$ years the amount in the account is $\$1643.55$.

Hence, option $\left(A\right)$ is the correct answer.