Continuous Compound Interest Concepts

The video tutorial explains the formula for calculating continuous compound interest, detailing each component: the total compound amount (A), the principal (P), the constant e, the interest rate (R), and the time in years (T). It provides a step-by-step example of calculating the total compound amount for an investment of $2,000 at a 7.5% interest rate over 5 years. The tutorial emphasizes the importance of using a calculator with the e function for accuracy and concludes with additional examples and a reminder not to round off the e constant.

What does the variable 'A' represent in the continuous compound interest formula?

• The time in years

• The yearly interest rate

• The total compound amount after a certain period

• The original amount invested

Which constant is used in the continuous compound interest formula and is approximately equal to 2.71828?

• Euler's number (e)

• Pi

• Golden ratio

• Planck's constant

In the example problem, what is the principal amount invested?

• $4,000

• $3,000

• $2,000

• $1,000

How is the yearly interest rate of 7.5% converted into a decimal for the formula?

• 0.75

• 0.075

• 0.0075

• 7.5

What is the value of 'T' in the example problem?

• 6 years

• 5 years

• 4 years

• 3 years

What is the first step in calculating the compound amount using the formula?

• Multiply the principal by the interest rate

• Multiply the interest rate by the time

• Raise e to the power of the product of the interest rate and time

• Add the principal to the interest

What is the result of raising e to the power of 0.375 in the example calculation?

• 2.71828

• 1.375

• 0.375

• 1.1454

After calculating e^0.375, what is the next step to find the total compound amount?

• Divide the result by the principal

• Subtract the principal from the result

• Multiply the result by the principal

• Add the principal to the result

What is the final compound amount after 5 years in the example problem?

• $2,399.90

• $2,299.90

• $2,199.90

• $2,299.00

What is a key tip mentioned for solving problems involving the e constant?

• Always round the e constant to two decimal places

• Use a calculator or software with the e function

• Estimate the e constant as 3

• Ignore the e constant in calculations