$1250 are deposited in an account with a 6.5% interest rate, compounded continuously. what is the balance…

Explanation:

Step1: Identify the continuous - compounding formula

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

Step2: Convert the interest rate to decimal

The interest rate $r = 6.5%=0.065$. The principal amount $P = 1250$ and the time $t = 8$ years.

Step3: Substitute the values into the formula

Substitute $P = 1250$, $r=0.065$, and $t = 8$ into the formula $A = Pe^{rt}$. So $A=1250\times e^{0.065\times8}$.

Step4: Calculate the exponent part

First, calculate $0.065\times8 = 0.52$. Then find $e^{0.52}$. Using a calculator, $e^{0.52}\approx1.68201$.

Step5: Calculate the final amount

Multiply $1250$ by $1.68201$. $A = 1250\times1.68201=2102.5125$.

Answer:

$2102.51$