Question

the bank offers a rate of 11%, compounded continuously, on any deposit that will not be removed for a minimum of 20 years. if you invest $10,000 with the bank, how much money can you expect to have in the account after 20 years? round your answer to the nearest cent (hundredth).

Explanation:

Step1: Recall the formula for continuous compounding

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

Step2: Identify the values of \( P \), \( r \), and \( t \)

We are given that \( P=\$10,000 \), \( r = 11\%=0.11 \), and \( t = 20 \) years.

Step3: Substitute the values into the formula

Substitute \( P = 10000 \), \( r=0.11 \), and \( t = 20 \) into the formula \( A=Pe^{rt} \). So we have \( A=10000\times e^{0.11\times20} \).
First, calculate the exponent: \( 0.11\times20 = 2.2 \). Then we have \( A = 10000\times e^{2.2} \).
We know that \( e^{2.2}\approx9.025013 \) (using a calculator to find the value of the exponential function).
Then \( A=10000\times9.025013=\$90250.13 \) (rounded to the nearest cent).

Answer:

\(\$90250.13\)