Question

jasmine invests $2,658 in a retirement account with a fixed annual interest rate of 9% compounded continuously. what will the account balance be after 15 years? your answer

Explanation:

Step1: Recall the formula for continuous compounding

The formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $t$ is the time the money is invested for in years.

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

Given that $P = 2658$, $r = 9\%= 0.09$, and $t = 15$.

Step3: Substitute the values into the formula

Substitute $P = 2658$, $r = 0.09$, and $t = 15$ into the formula $A = Pe^{rt}$. So we have $A=2658\times e^{0.09\times15}$.

Step4: Calculate the exponent

First, calculate the exponent $0.09\times15 = 1.35$.

Step5: Calculate the value of $e^{1.35}$

We know that $e^{1.35}\approx3.85742553$.

Step6: Calculate the value of A

Multiply $2658$ by $e^{1.35}$: $A = 2658\times3.85742553\approx2658\times3.8574\approx10252.97$.

Answer:

The account balance after 15 years will be approximately $\$10252.97$ (or more precisely, depending on the precision of $e^{1.35}$ used, but this is a reasonable approximation).