harper invested $3,200 in an account paying an interest rate of 7% compounded continuously. assuming no…

harper invested $3,200 in an account paying an interest rate of 7% compounded continuously. assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 6 years?

harper invested $3,200 in an account paying an interest rate of 7% compounded continuously. assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 6 years?

Answer

Explanation:

Step1: Recall continuous - compounding formula

The formula for continuous - compounding is $A = Pe^{rt}$, where $A$ is the amount of money in the account after $t$ years, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal form), and $t$ is the number of years.

Step2: Convert the interest rate to decimal

Given $r = 7%=0.07$, $P = 3200$, and $t = 6$.

Step3: Substitute values into the formula

$A=3200\times e^{0.07\times6}$. First, calculate the exponent: $0.07\times6 = 0.42$. Then, find the value of $e^{0.42}$. Using a calculator, $e^{0.42}\approx1.52196$. Next, multiply by the principal: $A = 3200\times1.52196=4870.272$.

Step4: Round to the nearest ten dollars

Rounding $4870.272$ to the nearest ten dollars gives $4870$.

Answer:

$4870$