Compound Interest
Compound interest calculates returns or costs where interest is repeatedly added to the principal, causing exponential growth that differs significantly from simple interest over time.
What You Need to Know
Key Concept Diagram
Compound interest formula: A = P(1 + r/n)^(nt), where P is principal, r is annual rate, n is compounding periods per year, t is time in years
Unlike simple interest, compound interest earns "interest on interest," accelerating growth over time
More frequent compounding periods (e.g., monthly vs. annually) result in higher effective interest
The Rule of 72 approximates the time to double an investment: divide 72 by the annual percentage rate
Key Vocabulary
Principal
The initial sum of money invested or borrowed before interest is applied
Compound interest
Interest calculated on the principal plus all previously accumulated interest
Compounding period
The frequency at which interest is calculated and added (annually, quarterly, monthly, daily)
Effective annual rate
The actual annual interest rate accounting for compounding within the year
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
$5 000 is invested at 4% per annum compounded annually for 3 years. What is the total amount?
Question 2
Using the Rule of 72, approximately how many years does it take to double an investment at 8% per annum?
Question 3
$2 000 is invested at 6% per annum compounded monthly for 2 years. Which expression correctly gives the final amount?
Key Concepts Summary
- ●Compound interest formula: A = P(1 + r/n)^(nt), where P is principal, r is annual rate, n is compounding periods per year, t is time in years
- ●Unlike simple interest, compound interest earns "interest on interest," accelerating growth over time
- ●More frequent compounding periods (e.g., monthly vs. annually) result in higher effective interest
- ●The Rule of 72 approximates the time to double an investment: divide 72 by the annual percentage rate