Question

tanisha invested $4,300 in an account paying an interest rate of 3.3% compounded continuously. assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 14 years?

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.
Here, $P = 4300$, $r = 0.033$ (since $3.3\%=0.033$), and $t = 14$.

Step2: Substitute the values into the formula

Substitute $P = 4300$, $r = 0.033$, and $t = 14$ into the formula $A = Pe^{rt}$.
So we have $A=4300\times e^{(0.033\times14)}$.

Step3: Calculate the exponent first

Calculate $0.033\times14 = 0.462$.

Step4: Calculate $e^{0.462}$

Using a calculator, $e^{0.462}\approx1.588$.

Step5: Calculate the final amount

Multiply $4300$ by $1.588$: $4300\times1.588 = 4300\times1.588 = 6828.4$ (approximate value, more accurately we can calculate $4300\times e^{0.462}$ directly).
Using a calculator for more precision: $4300\times e^{0.462}\approx4300\times1.588031\approx6828.5333$.
Rounding to the nearest cent (two decimal places), we get $6828.53$.

Answer:

$\$6828.53$