### Compound Interest Growth Calculation**Problem Statement:**How many years will it take for an initial investment of $20,000 to grow to $50,000? Assume a rate of interest of 11% compounded continuously.**Solution:**The formula for continuous compounding is given by:\[ A = P e^{rt} \]where:- $ A $ is the amount of money accumulated after n years, including interest.- $ P $ is the principal amount (the initial amount of money, which is $20,000).- $ r $ is the annual interest rate (decimal), which in this case is 11%, or 0.11.- $ t $ is the time the money is invested for in years.- $ e $ is the base of the natural logarithm, approximately equal to 2.71828.We need to solve for $ t $ when $ A $ (the final amount) is $50,000.So,\[ 50,000 = 20,000 \times e^{0.11 t} \]Divide both sides by 20,000:\[ \frac{50,000}{20,000} = e^{0.11 t} \]Simplify:\[ 2.5 = e^{0.11 t} \]Taking the natural logarithm on both sides:\[ \ln(2.5) = \ln(e^{0.11 t}) \]By the properties of logarithms:\[ \ln(2.5) = 0.11 t \]Therefore,\[ t = \frac{\ln(2.5)}{0.11} \]Calculate the value (using a calculator):\[ t \approx \frac{0.916}{0.11} \]\[ t \approx 8.33 \]So, it will take about 8.33 years for the investment to grow to $50,000.**Final Answer:**It will take about $\boxed{8.33}$ years for the investment to grow to $50,000. Please enter your answer in the box and then click "Check Answer". **Investment Growth Calculation****Problem Statement:**How many years will it take for an initial investment of $20,000 to grow to $50,000? Assume a rate of interest of 11% compounded continuously.**Solution:**It will take about _______ years for the investment to grow to $50,000. *(Round to two decimal places as needed.)***Input Instructions:**Enter your answer in the answer box and then click Check Answer. *(Buttons for clearing the answer and checking the answer are also present.)*

Name: ### Compound Interest Growth Calculation**Problem Statement:**How man
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: ### Compound Interest Growth Calculation**Problem Statement:**How many years will it take for an initial investment of $20,000 to grow to $50,000? Assume a rate of interest of 11% compounded continuously.**Solution:**The formula for continuous compo