Question

elise opened a savings account and deposited $800.00 as principal. the account earns 5% interest, compounded continuously. what is the balance after 1 year? round your answer to the nearest cent.

Explanation:

Step1: Recall the formula for continuous compounding

The formula for continuous compounding is $A = Pe^{rt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $t$ is the time in years, and $e$ is the base of the natural logarithm (approximately $2.71828$).

Step2: Identify the values of P, r, and t

Given that $P = 800$, $r = 5\%= 0.05$, and $t = 1$ year.

Step3: Substitute the values into the formula

Substitute $P = 800$, $r = 0.05$, and $t = 1$ into the formula $A = Pe^{rt}$:
\[
A=800\times e^{0.05\times1}
\]
\[
A = 800\times e^{0.05}
\]

Step4: Calculate the value of $e^{0.05}$ and then find A

We know that $e^{0.05}\approx1.051271096$. So,
\[
A=800\times1.051271096
\]
\[
A\approx841.016877
\]

Answer:

$\$841.02$ (rounded to the nearest cent)