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 = $1,500, r = 3.2%, t = 7 years; compounded continuously a = $ (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 = $1,500, r = 3.2%, t = 7 years; compounded continuously a = $ (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

Given $r = 3.2%$, convert it to decimal: $r=0.032$. The principal $P = 1500$ and $t = 7$.

Step3: Substitute values into the formula

Substitute $P = 1500$, $r=0.032$, and $t = 7$ into the formula $A = Pe^{rt}$. So $A=1500\times e^{(0.032\times7)}$.

Step4: Calculate the exponent

First, calculate $0.032\times7 = 0.224$. Then $A = 1500\times e^{0.224}$.

Step5: Evaluate the exponential and multiply

We know that $e^{0.224}\approx1.2518$. Then $A = 1500\times1.2518=1877.7$.

Answer:

$1877.70$