Compound Interest: The Maths Behind Growing Your Wealth

What Is Compound Interest?

Compound interest means you earn interest on your interest. Unlike simple interest (which earns on principal only), compound interest earns on the growing total — principal plus accumulated interest.

The Compound Interest Formula

A = P × (1 + r/n)^(n×t)

Where:

A = Final amount

P = Principal (initial investment)

r = Annual interest rate (decimal)

n = Compounding periods per year (12 for monthly, 4 for quarterly, 1 for annually)

t = Time in years

Example: Rs 1 lakh invested at 12% per year, compounded monthly for 10 years:

A = 1,00,000 × (1 + 0.12/12)^(12×10) = 1,00,000 × (1.01)^120 = Rs 3,30,039

The Impact of Time: Why Starting Early Matters

Compare two investors, both saving Rs 5,000/month at 12% CAGR:

Ravi starts at age 25, stops at 35 (10 years of investing): Invested Rs 6 lakh. Portfolio at age 60: Rs 1.76 crore.

Priya starts at age 35, invests until 60 (25 years of investing): Invested Rs 15 lakh. Portfolio at age 60: Rs 94 lakh.

Ravi invested less than half what Priya invested but ended up with nearly double at retirement — just by starting 10 years earlier.

Rule of 72: Quick Mental Maths

Divide 72 by the annual interest rate to estimate how many years it takes to double your money.

At 8% return: 72 ÷ 8 = 9 years to double

At 12% return: 72 ÷ 12 = 6 years to double

At 6% return: 72 ÷ 6 = 12 years to double

Compound Frequency Matters (But Less Than You Think)

Monthly compounding vs annual compounding on Rs 1 lakh at 10% for 20 years:

Annual compounding: Rs 6.73 lakh

Monthly compounding: Rs 7.33 lakh

The difference is real but modest. The interest rate and time invested matter far more than compounding frequency.