find the present value of $4000 payable at the end of 2 years, if money may be invested at 7% with interest…

Explanation:

Step1: Recall continuous - compounding formula

The formula for continuous - compounding is $A = Pe^{rt}$, where $A$ is the future value, $P$ is the present value, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. We want to find $P$, and we can re - arrange the formula to $P=\frac{A}{e^{rt}}$.

Step2: Identify the values of $A$, $r$, and $t$

We are given that $A = 4000$, $r=0.07$ (since $7%=0.07$), and $t = 2$.

Step3: Substitute the values into the formula

$P=\frac{4000}{e^{0.07\times2}}=\frac{4000}{e^{0.14}}$.

Step4: Calculate the value

Using a calculator, $e^{0.14}\approx1.15027$, so $P=\frac{4000}{1.15027}\approx3477.46$.

Answer:

$3477.46$