Question

exercise 4.1.9
if $500 is invested in an account earning 12% compounded continuously, find the value after 2 years.
value = $
important topics of this section

• percent growth
• exponential functions: finding equations; interpreting equations; graphs
• exponential growth & decay
• compounded interest
• annual percent yield
• continuous growth

question help: message instructor post to forum

Explanation:

Step1: Identify the formula for continuous compounding

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: Substitute the given values into the formula

Given \( P=\$500\), \( r = 0.12\) (since \( 12\%=0.12\)), and \( t = 2\) years.
Substitute into \( A = Pe^{rt}\):
\( A=500\times e^{0.12\times2}\)
\( A = 500\times e^{0.24}\)

Step3: Calculate the value of \( e^{0.24}\)

Using a calculator, \( e^{0.24}\approx1.271249\)

Step4: Calculate the final amount \( A\)

\( A=500\times1.271249 = 635.6245\approx635.62\)

Answer:

\(635.62\)