if you invest $9000 at 3.15% interest compounded continuously, how much will you have in 7 yrs?

Explanation:

Step1: Identify the continuous - compounding formula

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: Convert the interest rate to decimal

The given interest rate is $3.15%$. To convert it to decimal, we divide by 100. So, $r=0.0315$. The principal $P = 9000$ and the time $t = 7$ years.

Step3: Substitute the values into the formula

Substitute $P = 9000$, $r=0.0315$, and $t = 7$ into the formula $A = Pe^{rt}$. We get $A=9000\times e^{0.0315\times7}$.

Step4: Calculate the exponent

First, calculate $0.0315\times7 = 0.2205$. Then, find the value of $e^{0.2205}$. Using a calculator, $e^{0.2205}\approx1.2479$.

Step5: Calculate the final amount

Multiply 9000 by $1.2479$. So, $A = 9000\times1.2479=11231.1$.

Answer:

$11231.1$