Question

moneysavers bank offers a savings account that earns 9.5% interest per year, compounded continuously. if mai deposits $3800, how much will she have in the account after two years, assuming she makes no withdrawals? do not round any intermediates computations, and round your answer to the nearest cent.

Explanation:

Step1: Recall continuous compounding formula

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.
Here, $P = 3800$, $r = 0.095$ (since 9.5% = 0.095), and $t = 2$.

Step2: Substitute values into the formula

Substitute the values into the formula: $A = 3800\times e^{0.095\times2}$.
First, calculate the exponent: $0.095\times2 = 0.19$.
So, $A = 3800\times e^{0.19}$.

Step3: Calculate the value of $e^{0.19}$ and then multiply by 3800

We know that $e^{0.19}\approx1.209279495$.
Then, $A = 3800\times1.209279495$.
Calculate the product: $3800\times1.209279495 = 4595.262081$.

Step4: Round to the nearest cent

Rounding 4595.262081 to the nearest cent gives 4595.26.

Answer:

$\$4595.26$