jae invested $3,500 at a rate of 2.25% compounded continuously in 2010. how much will be in the account in…

Explanation:

Step1: Identify the 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: Determine the values of $P$, $r$, and $t$

$P=$3500$, $r = 0.0225$ (since $2.25%=0.0225$), and $t=2025 - 2010=15$ years.

Step3: Substitute the values into the formula

$A = 3500\times e^{0.0225\times15}$. First, calculate the exponent: $0.0225\times15 = 0.3375$. Then, find $e^{0.3375}$. Using a calculator, $e^{0.3375}\approx1.39096$. Multiply by the principal: $A = 3500\times1.39096\approx4868.36$.

Answer:

$4868.36$