bonnie opened a savings account 2 years ago. the account earns 5% interest, compounded continuously. if the…

bonnie opened a savings account 2 years ago. the account earns 5% interest, compounded continuously. if the current balance is $200.00, how much did she deposit initially? use the formula $a = pe^{rt}$, where $a$ is the balance (final amount), $p$ is the principal (starting amount), $e$ is the base of natural logarithms ($\\approx2.71828$), $r$ is the interest rate expressed as a decimal, and $t$ is the time in years. round your answer to the nearest cent.

bonnie opened a savings account 2 years ago. the account earns 5% interest, compounded continuously. if the current balance is $200.00, how much did she deposit initially? use the formula $a = pe^{rt}$, where $a$ is the balance (final amount), $p$ is the principal (starting amount), $e$ is the base of natural logarithms ($\\approx2.71828$), $r$ is the interest rate expressed as a decimal, and $t$ is the time in years. round your answer to the nearest cent.

Answer

Explanation:

Step1: Identify given values

$A = 200$, $r=0.05$, $t = 2$

Step2: Rearrange the formula for $P$

Given $A = Pe^{rt}$, we can solve for $P$ as $P=\frac{A}{e^{rt}}$.

Step3: Substitute values into the formula for $P$

$P=\frac{200}{e^{0.05\times2}}$ $P=\frac{200}{e^{0.1}}$ Since $e^{0.1}\approx1.10517$, then $P=\frac{200}{1.10517}\approx180.97$

Answer:

$180.97$