Continuous Compound Interest Concepts

The video tutorial explains the formula for calculating continuous compound interest, which is A = P * e^(r*T). It breaks down each component: A is the total amount, P is the principal, e is a constant approximately 2.71828, r is the annual interest rate, and T is the time in years. An example is provided where $2,000 is invested at a 7.5% interest rate compounded continuously over 5 years. The video demonstrates using a calculator to compute the result, emphasizing the importance of not rounding the e constant. The final calculated amount is approximately $299.90.

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

• The yearly interest rate

• The time in years

• The original amount invested

• The total compound amount after a certain period

In the formula for continuous compound interest, what does 'P' stand for?

• The numerical constant

• The yearly interest rate

• The original amount invested or borrowed

• The total compound amount

What is the approximate value of the constant 'e' used in continuous compound interest calculations?

• 3.14159

• 1.41421

• 1.61803

• 2.71828

Why is it important to use a calculator with the 'e' function for continuous compound interest problems?

• Because 'e' is a very small number

• Because 'e' is an irrational number that goes on forever

• Because 'e' is a whole number

• Because 'e' is a negative number

In the example problem, what is the yearly interest rate converted to a decimal?

• 0.0075

• 7.5

• 0.075

• 0.75

How many years is the investment period in the example problem?

• 3 years

• 5 years

• 7 years

• 10 years

What is the first step in solving the example problem using the formula?

• Multiply the principal by the interest rate

• Calculate the value of 'e' raised to the power of the product of the interest rate and time

• Convert the interest rate to a decimal

• Multiply the interest rate by the time

What is the result of multiplying 0.075 by 5 in the example problem?

• 37.5

• 0.0375

• 3.75

• 0.375

After calculating 'e' raised to the power of 0.375, what is the next step in the example problem?

• Add the principal to the result

• Subtract the principal from the result

• Multiply the result by the principal

• Divide the result by the principal

What is the final compound amount calculated in the example problem?

• $2,000.00

• $2,375.00

• $2,299.90

• $2,145.40