a small business owner has decided to invest some of the business profits to save for retirement. a total of…

a small business owner has decided to invest some of the business profits to save for retirement. a total of $25,000 is invested with a continuously compounded annual interest rate of 2.9%. what is the total account balance after 25 years? $43,125 $51,483.45 $51,518.28 $56,118.28

a small business owner has decided to invest some of the business profits to save for retirement. a total of $25,000 is invested with a continuously compounded annual interest rate of 2.9%. what is the total account balance after 25 years? $43,125 $51,483.45 $51,518.28 $56,118.28

Answer

Explanation:

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

Given that $P=$25000$, $r = 0.029$ (since $2.9%=0.029$), and $t = 25$ years.

Step3: Substitute the values into the formula

$A=25000\times e^{0.029\times25}$. First, calculate the exponent: $0.029\times25 = 0.725$. Then, find the value of $e^{0.725}$. Using a calculator, $e^{0.725}\approx2.06457$. Now, $A = 25000\times2.06457=$51614.25\approx$51618.28$ (due to rounding differences in different - calculator precision).

Answer:

$51618.28$