Question

aaliyah invested $680 in an account paying an interest rate of 5.6% compounded continuously. assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 6 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.

Step2: Identify the values

Here, $P = 680$, $r = 5.6\%=0.056$, and $t = 6$.

Step3: Substitute the values into the formula

Substitute $P = 680$, $r = 0.056$, and $t = 6$ into $A = Pe^{rt}$:
$A = 680\times e^{0.056\times6}$
First, calculate the exponent: $0.056\times6 = 0.336$
Then, $A = 680\times e^{0.336}$
Using a calculator, $e^{0.336}\approx1.3989$
So, $A\approx680\times1.3989$

Step4: Calculate the final amount

$680\times1.3989 = 951.252$

Answer:

$\$951.25$ (rounded to the nearest cent)