Modeling Equations for Continuous Compounding and Solving for Time

This video tutorial covers solving for time in continuously compounding functions. It begins with an introduction to compounding interest, using examples of quarterly, monthly, and weekly compounding. The lesson then reviews solving exponential equations using logarithms, highlighting the differences between log base 10 and natural log. The concept of continuous compounding is explored, demonstrating how the expression approaches the irrational number e. Finally, practical applications are discussed, including calculating the future value of an investment with continuous compounding and determining the time needed to reach a financial goal.

If you invest $2,000 at 6% interest for five years, how much will you have if compounded quarterly?

• $2,693

• $3,000

• $2,500

• $2,800

What is the inverse operation of an exponential function with base 10?

• Division

• Logarithm base 10

• Multiplication

• Natural Logarithm

Which of the following is the natural logarithm of 100?

• 4.6051702

• 10

• 100

• 2

What happens to the amount of money you make as you increase the frequency of compounding?

• It doubles

• It decreases

• It remains the same

• It increases but by smaller amounts

What is the approximate value of e used for continuous compounding?

• 2.00

• 1.61

• 3.14

• 2.71

If you invest $10,000 at 8% interest compounded continuously, how much will it be worth in 10 years?

• $20,000

• $25,000

• $18,000

• $22,255

How long will it take for an account to grow to $1,000,000 if $10,000 is invested at 8% interest compounded continuously?

• 45 years

• 58 years

• 60 years

• 70 years