Learn how long to invest your money compounded continuously

The video tutorial explains how to calculate the number of years needed to grow $100 to $1000 using continuous compounding at an 8% interest rate. It introduces the formula FV = P * e^(RT), defines the variables, and demonstrates solving for time using natural logarithms. The calculation shows it takes approximately 29 years, highlighting the power of compounding.

What is the formula used to calculate the future value in continuous compounding?

• FV = P * E^(R/T)

• FV = P * (1 + R)^T

• FV = P * E^(RT)

• FV = P * (1 + RT)

In the given problem, what is the present value (P) used in the formula?

• $50

• $100

• $500

• $1000

After dividing both sides by 100, what equation do we get?

• 1000 = E^(0.08T)

• 10 = E^(T)

• 100 = E^(0.08T)

• 10 = E^(0.08T)

What mathematical operation is used to solve for T in the equation 10 = E^(0.08T)?

• Dividing by 10

• Multiplying by 0.08

• Taking the natural logarithm

• Taking the square root

Approximately how many years will it take to grow $100 to $1000 at an 8% continuous compounding rate?

• 35 years

• 20 years

• 25 years

• 29 years