Continuous Interest and Euler's Number

This lesson covers continuous interest, explaining the formula A = P * e^(rt) where P is the principal, r is the annual interest rate as a decimal, and t is time in years. The video provides three examples: calculating future balance, determining time to reach a target balance, and finding the initial investment needed for a desired future balance. Each example uses the continuous interest formula and demonstrates the use of logarithms for solving equations involving exponents.

What is the formula for calculating the amount in an account with continuous interest?

• A = P(1 + rt)

• A = P * (1 + r)^t

• A = P * e^(rt)

• A = P(1 + r/n)^(nt)

What is Euler's number approximately equal to?

• 1.41421

• 1.61803

• 2.71828

• 3.14159

If you invest $2,500 at 4% continuous interest, what will the balance be after 4 years?

• $2,800.00

• $2,933.78

• $2,950.00

• $3,000.00

In the first example, what is the decimal representation of a 4% interest rate?

• 0.04

• 0.4

• 0.004

• 4.0

How long will it take for $4,000 to grow to $6,000 at 6% continuous interest?

• 7.2 years

• 6.5 years

• 5.5 years

• 6.76 years

In the second example, what is the principal amount?

• $4,000

• $5,000

• $6,000

• $3,000

What is the continuous interest rate in the third example?

• 4%

• 6%

• 5%

• 5.5%

How much must you invest today to have $10,000 in 5 years at 5.5% continuous interest?

• $7,500.00

• $7,595.72

• $8,000.00

• $7,800.00

In the third example, what is the future amount desired?

• $10,000

• $5,000

• $7,500

• $8,000

What is the time period considered in the third example?

• 5 years

• 4 years

• 6 years

• 3 years