if $15,000 is invested at a rate of 4.75% compounded continuously for 25 years, what is the final value of…

Explanation:

Step1: Identify the continuous - compounding formula

The formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years.

Step2: Convert the percentage to decimal

Given $r = 4.75%=0.0475$, $P=$15000$, and $t = 25$ years.

Step3: Substitute values into the formula

$A=15000\times e^{0.0475\times25}$. First, calculate the exponent: $0.0475\times25 = 1.1875$. Then, find $e^{1.1875}$. Using a calculator, $e^{1.1875}\approx3.278874$. Now, $A = 15000\times3.278874$. $A=49183.11$.

Answer:

$49,183.11$