scott wants to buy a bond that will mature to $4500 in seven years. how much should he pay for the bond now…

Answer:

$3251.98$

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 (initial) amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. We need to solve for $P$, 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 $A = 4500$, $r=0.04$ (since $4%=0.04$), and $t = 7$.

Step3: Substitute the values into the formula

$P=\frac{4500}{e^{0.04\times7}}=\frac{4500}{e^{0.28}}$.

Step4: Calculate the value of $P$

Using a calculator, $e^{0.28}\approx1.32924766$, and $\frac{4500}{1.32924766}\approx3251.98$.