example #2\nlets consider the same situation from the previous example.\nyour parents invest $1,000 at 5%…

example #2\nlets consider the same situation from the previous example.\nyour parents invest $1,000 at 5%, but now the money is compounded continuously for 18 years.\nnow how much money would you have?\na = pe^(rt)\na = 1000e^(.05 * 18)

example #2\nlets consider the same situation from the previous example.\nyour parents invest $1,000 at 5%, but now the money is compounded continuously for 18 years.\nnow how much money would you have?\na = pe^(rt)\na = 1000e^(.05 * 18)

Answer

Explanation:

Step1: Identify the formula for continuous - compounding

The formula for continuous - compounding is $A = Pe^{rt}$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years.

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

Given that $P=$1000$, $r = 0.05$ (since $5%=0.05$), and $t = 18$ years.

Step3: Substitute the values into the formula

Substitute $P = 1000$, $r=0.05$, and $t = 18$ into the formula $A = Pe^{rt}$. We get $A=1000e^{(0.05\times18)}$.

Step4: Calculate the exponent

First, calculate $0.05\times18 = 0.9$. Then we have $A = 1000e^{0.9}$.

Step5: Evaluate $e^{0.9}$ and find $A$

We know that $e^{0.9}\approx2.45960311$. So $A=1000\times2.45960311\approx2459.60$.

Answer:

$$2459.60$