find the amount in the account for the given principal, interest rate, time, and compounding period. p =…

find the amount in the account for the given principal, interest rate, time, and compounding period. p = $1,200, r = 3.5%, t = 7 years; compounded continuously\na = $ \n(type an integer or decimal rounded to the nearest cent as needed.)

find the amount in the account for the given principal, interest rate, time, and compounding period. p = $1,200, r = 3.5%, t = 7 years; compounded continuously\na = $ \n(type an integer or decimal rounded to the nearest cent as needed.)

Answer

Explanation:

Step1: Recall continuous - compounding formula

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

Step2: Convert the interest rate to decimal form

Given $r = 3.5%$, we convert it to decimal form: $r=0.035$. We know that $P = 1200$ and $t = 7$.

Step3: Substitute the values into the formula

Substitute $P = 1200$, $r = 0.035$, and $t = 7$ into the formula $A = Pe^{rt}$. So $A=1200\times e^{0.035\times7}$.

Step4: Calculate the exponent part

First, calculate $0.035\times7 = 0.245$. Then, find the value of $e^{0.245}$. Using a calculator, $e^{0.245}\approx1.27762$.

Step5: Calculate the final amount

Multiply $1200$ by $1.27762$. $A = 1200\times1.27762=1533.144$.

Answer:

$1533.14$