Compound Interest and Exponential Growth

This lesson covers exponential models, focusing on compound interest and continuous compounding. It explains the formulas for calculating compound interest with different compounding frequencies and demonstrates the PERT formula for continuous compounding. Examples include calculating future values of investments and deriving exponential models from data points.

What is the main focus of lesson 62?

• Linear models

• Logarithmic models

• Quadratic models

• Exponential models

In the exponential growth formula y = a * b^x, what does 'a' represent?

• The growth rate

• The initial value

• The time period

• The final value

If a necklace costs $250 and increases in value by 2% per year, what is the growth factor?

• 250

• 2.50

• 0.02

• 1.02

What is the formula for compound interest?

• A = P * e^(rt)

• A = P * (1 + r/n)^(nt)

• A = P * (1 - r/n)^(nt)

• A = P * (1 + rt)

In the compound interest formula, what does 'n' represent?

• The total time in years

• The interest rate

• The principal amount

• The number of compounding periods per year

What is the PERT formula used for?

• Calculating simple interest

• Calculating quarterly interest

• Calculating continuously compounded interest

• Calculating annual interest

What is the approximate value of 'e' used in continuous compounding?

• 3.14

• 2.718

• 0.577

• 1.618

If Tamira invests $5000 at 4% annual interest, how much will she have after 3 years if compounded annually?

• $5,624.32

• $5,500.00

• $5,630.81

• $5,000.00

How does increasing the frequency of compounding affect the amount of money earned?

• It doubles the amount

• It has no effect

• It increases the amount

• It decreases the amount

Regina invests $12,600 at 3.2% annual interest compounded continuously. What will be the value after 12 years?

• $18,498.63

• $15,000.00

• $17,500.00

• $20,000.00