present value. a promissory note will pay $75,000 at maturity 4 years from now. how much should you be…

Explanation:

Step1: Identify the 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 $P$, so we can rewrite the formula as $P=\frac{A}{e^{rt}}$.

Step2: Convert the given values to the appropriate form

We are given that $A = 75000$, $r=0.06$ (since $6%=0.06$), and $t = 4$.

Step3: Substitute the values into the formula

$P=\frac{75000}{e^{0.06\times4}}=\frac{75000}{e^{0.24}}$.

Step4: Calculate the value of $P$

Using a calculator, $e^{0.24}\approx1.271249$, so $P=\frac{75000}{1.271249}\approx58998$.

Answer:

$58998$