Exploring Continuous Compounds in Compound Interest

This video tutorial explains how to calculate compound interest with continuous compounding. It introduces the formula A = Pe^rt, where A is the final amount, P is the principal, e is the constant approximately equal to 2.718, r is the rate as a decimal, and t is the time in years. The video provides two examples to demonstrate the calculation process, emphasizing careful use of calculators to ensure correct exponentiation.

What does continuous compounding refer to in finance?

• A fixed rate of interest applied annually

• Compounding interest at set intervals

• Compounding interest continuously over time

• A method of reducing the principal amount

What is the value of the mathematical constant 'e' used in the continuous compounding formula?

• 6.02214

• 3.14159

• 2.71828

• 1.60218

In the formula A = Pe^(rt), what does 'P' represent?

• The rate of interest

• The final amount

• The time in years

• The principal amount

How should the rate be expressed in the formula for continuous compounding?

• As a percentage

• As a decimal

• As an integer

• As a fraction

What is the purpose of the 'e' button on calculators in the context of continuous compounding?

• To calculate exponential growth

• To enter the principal amount

• To specify the number of years

• To adjust the interest rate

What is the final amount after 20 years for an initial investment of $25,000 at an 11.5% interest rate?

• $249,354.56

• $300,000.00

• $230,000.00

• $275,000.00

What does the 't' in the formula A = Pe^(rt) stand for?

• Total interest

• Time in years

• Transaction number

• Tax rate

What is the final amount after 10 years for an initial investment of $13,000 at a 4% interest rate?

• $19,393.72

• $17,500.00

• $20,000.00

• $15,000.00

Which key phrase indicates the use of the continuous compounding formula?

• Compounded annually

• Compounded monthly

• Compounded continuously

• Compounded weekly

What should you be careful about when entering the continuous compounding formula into a calculator?

• Dividing the principal by the rate

• Using the percentage form of the rate

• Separating the variables with commas

• Ensuring the exponent is calculated together