Continuously Compounded Interest Concepts

The video tutorial explains the difference between continuous and discrete growth models, focusing on how to convert between continuously and annually compounded interest rates. It demonstrates the use of natural logarithms to solve for the continuous interest rate given a discrete rate and vice versa. The tutorial includes example calculations and discusses the implications of interest rate differences, emphasizing that continuous rates are typically lower than discrete rates due to the nature of compounding.

What is the equation for a continuous growth model?

• V = A * e^(i)

• V = A * (1 + rt)

• V = A * (1 + i)^t

• V = A * e^(rt)

In a discrete growth model, what does 'i' represent?

• Daily compounded interest rate

• Annually compounded interest rate

• Continuously compounded interest rate

• Monthly compounded interest rate

How can you find the continuously compounded interest rate from an annually compounded rate?

• Multiply by e

• Add 1 and take the natural log

• Divide by e

• Subtract 1 and take the natural log

What is the formula to solve for 'r' when 'i' is known?

• r = 1 + ln(i)

• r = ln(i)

• r = e^(1 + i)

• r = ln(1 + i)

If the annually compounded interest rate is 0.09, what is the equivalent continuously compounded rate?

• 0.082

• 0.09

• 0.0862

• 0.092

Why is the continuously compounded interest rate typically lower than the annually compounded rate?

• Because it compounds less frequently

• Because it is calculated using a different base

• Because it compounds more frequently

• Because it is always set lower by banks

What is the formula to convert a continuously compounded rate to an annually compounded rate?

• i = e^r - 1

• i = ln(r) + 1

• i = r * e

• i = e^(r + 1)

If r is 0.06, what is the equivalent annually compounded interest rate?

• 0.062

• 0.0618

• 0.065

• 0.06