your bank is willing to give you an interest rate of 8%, compounded continuously, on any investment made…

your bank is willing to give you an interest rate of 8%, compounded continuously, on any investment made with their money market accounts. you have $3,200 to deposit into the bank. what is your expected return if you leave your money in this bank for 4 years? round your answer to the nearest cent (hundredth)

your bank is willing to give you an interest rate of 8%, compounded continuously, on any investment made with their money market accounts. you have $3,200 to deposit into the bank. what is your expected return if you leave your money in this bank for 4 years? round your answer to the nearest cent (hundredth)

Answer

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 annual interest rate $r = 8%=0.08$, the principal amount $P = 3200$, and the time $t = 4$ years.

Step3: Substitute the values into the formula

$A=3200\times e^{0.08\times4}$. First, calculate the exponent: $0.08\times4 = 0.32$. Then, find $e^{0.32}$. Using a calculator, $e^{0.32}\approx1.3771277$. So, $A = 3200\times1.3771277$.

Step4: Calculate the final amount

$A=3200\times1.3771277 = 4406.80864$.

Step5: Round the answer

Rounding to the nearest cent, $A\approx4406.81$.

Answer:

$4406.81$