Simple vs Compound Interest: Which Makes You Richer? (Formulas & Real Examples)

The Fundamental Comparison

Whether you are saving money in fixed deposits, investing in mutual funds, or paying off student loans, interest is the price of money over time.

• Simple Interest: Linear growth. You only earn interest on what you initially deposited.
• Compound Interest: Exponential growth. You earn interest on your principal plus interest on all previous interest payments.

1. Simple Interest Mathematical Formula

$$SI = \frac{P \times R \times T}{100}$$

Where:

• P = Principal amount
• R = Annual interest rate (percentage)
• T = Time period in years

Example:

Investing ₹1,00,000 at 8% simple interest for 10 years:

• Interest Earned = (1,00,000 × 8 × 10) ÷ 100 = ₹80,000
• Total Maturity Value = ₹1,80,000

2. Compound Interest Mathematical Formula

$$A = P \left(1 + \frac{r}{n}\right)^{n \times t}$$

Where:

• A = Final amount
• P = Initial principal balance
• r = Annual interest rate (decimal)
• n = Compounding frequency per year (1 for annual, 4 for quarterly, 12 for monthly, 365 for daily)
• t = Time period in years

Example:

Investing the same ₹1,00,000 at 8% compounded annually for 10 years:

• Maturity Value = 1,00,000 × (1 + 0.08)^10 = ₹2,15,892
• Compound Interest Earned = ₹1,15,892

Net Difference: Compound interest generates ₹35,892 more (+44.8% extra profit) than simple interest on the exact same capital and rate!

3. The Power of the Rule of 72

To quickly calculate how fast an investment doubles under compound interest:

$$\text{Years to Double} \approx \frac{72}{\text{Annual Interest Rate}}$$

• At 6% interest: Doubled in 72 ÷ 6 = 12 years
• At 9% interest: Doubled in 72 ÷ 9 = 8 years
• At 12% interest: Doubled in 72 ÷ 12 = 6 years

Simulate multiple compounding frequencies and deposit schedules using our **Interest Calculator**.