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Lesson 11

Simple & Compound Interest

Master interest rate calculations for savings and loans.

  • master

Formula

I = P × r × t

📚 Simple & Compound Interest

Interest calculations are fundamental to finance. Understanding the difference between simple and compound interest is crucial for loans, savings, and investments.

Simple Interest:

I = P × r × t

Where: I = Interest, P = Principal, r = rate (as decimal), t = time (years)

Example: Simple Interest

You deposit $5,000 at 4% annual simple interest for 3 years.

1
I = $5,000 × 0.04 × 3
2
I = $600

Total amount after 3 years: $5,000 + $600 = $5,600

Compound Interest:

A = P(1 + r/n)^(nt)

Where: A = Final amount, P = Principal, r = rate, n = compounds per year, t = years

Example: Compound Interest (Annual)

You invest $1,000 at 5% annual interest compounded yearly for 2 years.

1
A = $1,000(1 + 0.05/1)^(1×2)
2
A = $1,000(1.05)^2 = $1,000 × 1.1025
3
A = $1,102.50

💡 Key Insight: With compound interest, you earn interest on your interest! This makes your money grow faster than simple interest over time.

Frequently Asked Questions

What is the difference between simple and compound interest?

Simple interest is paid only on the principal: $1,000 at 5% earns $50 every year. Compound interest is also paid on earlier interest, so year two earns 5% of $1,050 = $52.50, and the gap grows every year.

What does APR mean?

The annual percentage rate is the yearly cost of borrowing, including interest and most fees, expressed as a percentage. It is the number to compare loans and credit cards by.

Practice

Work each one out, then check yourself.

  1. Calculate the simple interest on $5,000 at 4% annual rate for 3 years.

    Hint: Use the formula I = P × r × t. Remember to convert 4% to 0.04

    Show answer

    600

  2. What's the compound amount (total A) of $1,000 at 5% compounded annually for 2 years?

    Hint: A = $1,000 × (1.05)^2. Calculate (1.05)^2 = 1.1025, then multiply by $1,000

    Show answer

    1102.5

Final Quiz

0/3

Test what you learned. Pick the correct answer for each question.

  1. $1,000 at 5% simple interest for 3 years yields how much interest?

    $1,000 at 5% simple interest for 3 years yields how much interest?

  2. $1,000 at 5% compounded annually for 3 years grows to:

    $1,000 at 5% compounded annually for 3 years grows to:

  3. Which earns more on $1,000 over 10 years at 6%?

    Which earns more on $1,000 over 10 years at 6%?