Understanding Compound Interest

This lesson covers how to calculate compound interest using an investment model. It begins with a problem involving a $5,000 investment at 6% interest compounded annually over 18 years. Key terms like principal and interest rate are explained. The lesson distinguishes between simple and compound interest, highlighting the exponential growth of compound interest. A step-by-step calculation is demonstrated, leading to a general formula for compound interest. The formula is applied to a new problem, reinforcing the concept.

What is the principal amount in the given problem?

• $6,300

• $5,300

• $6,000

• $5,000

What is the interest rate converted to a decimal for a 6% annual interest?

• 0.6

• 0.006

• 0.06

• 6.0

How does compound interest differ from simple interest?

• Simple interest grows faster than compound interest

• Compound interest grows exponentially, simple interest grows linearly

• Compound interest is linear, simple interest is exponential

• Both grow at the same rate

How much interest is earned in the first year on a $5,000 investment at 6% annual interest?

• $300

• $600

• $30

• $60

What happens to the principal amount each year in compound interest?

• It remains the same

• It increases by a percentage of the current principal

• It increases by a fixed amount

• It decreases

What is the formula for calculating compound interest?

• A = P + rt

• A = P(1 + rt)

• A = P(1 - r)^t

• A = P(1 + r)^t

If you invest $2,000 at 4% interest compounded annually, how much will you have after 6 years?

• $2,800

• $2,531

• $2,400

• $3,000