find the present value of the following future amount. $200,000 at 9% compounded annually for 25 years. what…

Explanation:

Step1: Recall compound - interest present - value formula

The formula for present value $PV$ when compounded annually is $PV=\frac{FV}{(1 + r)^n}$, where $FV$ is the future value, $r$ is the annual interest rate (in decimal form), and $n$ is the number of years.

Step2: Convert the interest rate to decimal

Given $r = 9%=0.09$, $FV = 200000$, and $n = 25$.

Step3: Substitute values into the formula

$PV=\frac{200000}{(1 + 0.09)^{25}}$

Step4: Calculate $(1 + 0.09)^{25}$

$(1 + 0.09)^{25}\approx8.62308066$.

Step5: Calculate the present value

$PV=\frac{200000}{8.62308066}\approx23193.91$.

Answer:

$23193.91$