How to use this guide
Work through each section step by step. Focus on understanding how interest is calculated and how time affects the growth of money.
Big idea: Simple interest is calculated only on the original amount, while compound interest is calculated on both the original amount and the accumulated interest.
Simple Interest
\[
\text{Simple Interest (SI)} = \text{interest calculated on the principal only}
\]
Simple interest is calculated only on the original amount of money (principal).
Example:
Principal = 1000, Rate = 5\%, Time = 2 years
Interest = 1000 × 5 × 2 ÷ 100 = 100
Try This
Simple Interest Formula
\[
SI = \frac{P \times R \times T}{100}
\]
Where:
- P = Principal
- R = Rate (%)
- T = Time (years)
Example:
\[
P = 2000,\quad R = 10\%,\quad T = 3
\]
\[
SI = \frac{2000 \times 10 \times 3}{100} = 600
\]
Compound Interest
\[
\text{Compound Interest} = \text{interest calculated on principal + accumulated interest}
\]
Compound interest increases faster because interest is added to the principal each period.
Example:
Principal = 1000, Rate = 10\%, Time = 2 years
Year 1 = 1100
Year 2 = 1210
Try This
Compound Interest Formula
\[
A = P(1 + \frac{R}{100})^T
\]
Where:
- A = Amount
- P = Principal
- R = Rate
- T = Time
Example:
\[
P = 1000,\quad R = 10\%,\quad T = 2
\]
\[
A = 1000(1.1)^2 = 1210
\]
\[
CI = A - P = 1210 - 1000 = 210
\]
Worksheet
Comparing Simple and Compound Interest
Simple Interest grows steadily.
Compound Interest grows faster over time.
Example:
P = 1000, R = 10\%, T = 2
SI = 200
CI = 210
Mixed Practice
Find SI:
\[
P = 1500,\quad R = 8\%,\quad T = 2
\]
\[
SI = 240
\]
Find CI:
\[
P = 2000,\quad R = 5\%,\quad T = 2
\]
\[
A = 2205
\]
\[
CI = 205
\]