present value. a promissory note will pay $45,000 at maturity 10 years from now. how much should you be…

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

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

We are given that $A = 45000$, $r=0.03$ (since $3%= 0.03$), and $t = 10$.

Step3: Substitute the values into the formula

$P=\frac{45000}{e^{0.03\times10}}=\frac{45000}{e^{0.3}}$.

Step4: Calculate the value of $P$

We know that $e^{0.3}\approx1.34986$, so $P=\frac{45000}{1.34986}\approx33333$.

Answer:

$33333$