How Compound Interest and SIP Work (with Math Breakdowns)

Albert Einstein famously described compound interest as the eighth wonder of the world: "He who understands it, earns it; he who doesn't, pays it."

Compound interest is the engine behind long-term wealth accumulation. Unlike simple interest—which only earns returns on the initial principal—compound interest earns returns on both the starting principal and all accumulated interest from prior periods.

Here is a clear mathematical walkthrough of how compounding works and how Systematic Investment Plans (SIP) harness it.

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1. The Standard Compound Interest Formula #

For a single lump-sum investment:

Where:

• A: Final accumulated amount.
• P: Initial principal deposit.
• r: Annual interest rate (in decimal, e.g., 8% = 0.08).
• n: Compounding frequency per year (e.g., 12 for monthly, 1 for annual).
• t: Duration in years.

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2. Systematic Investment Plan (SIP) Compounding Formula #

When investing a fixed amount regularly (e.g., monthly deposits):

Where:

• M: Maturity amount.
• P: Monthly investment amount.
• i: Periodic interest rate ($r / 12$).
• n: Total number of monthly contributions ($t \times 12$).

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3. The Power of Time: An Illustrative Example #

Consider two investors:

• Investor A: Invests $500/month$ from age 25 to 35 (10 years total,60,000 invested), then stops adding money and lets it grow at 10% annual return until age 60.
• Investor B: Waits until age 35, then invests $500/month$ every month for 25 years until age 60 (150,000 invested) at the same 10% annual return.

Result at Age 60:

• Investor A: Accumulates ~$780,000$ despite investing only60,000.
• Investor B: Accumulates ~$660,000$ despite investing150,000.

Starting early allows compounding cycles to do the heavy lifting.

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Summary & Calculation Tools #

Understanding the mathematics behind compounding empowers you to set realistic financial milestones. To run custom scenarios, test your numbers on the free Burnjet Compound Interest Calculator and SIP Calculator.