Compound Interest Formula — Complete Guide with Examples

Albert Einstein reportedly called compound interest the eighth wonder of the world: "He who understands it, earns it; he who doesn't, pays it." Whether or not he said it, the principle is undeniable. Compound interest is the engine behind every long-term investment — from Fixed Deposits and PPF to mutual funds and retirement corpus plans. Understanding the formula is the first step to making your money work harder.

This guide breaks down the compound interest formula, compounding frequency, the Rule of 72, and real worked examples. Use our Compound Interest Calculator to compute returns instantly.

What Is Compound Interest?

Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest, which grows linearly, compound interest grows exponentially — meaning the growth accelerates as time passes. The longer your money compounds, the more dramatic the acceleration.

The Compound Interest Formula

The standard formula is:

A = P × (1 + r/n)^(n×t)

Where:

• A = Final amount (principal + interest)
• P = Initial principal
• r = Annual interest rate (in decimal; 8% = 0.08)
• n = Number of times interest is compounded per year
• t = Number of years

The compound interest earned = A − P.

Compounding Frequency Matters

The value of n dramatically affects your returns. Common compounding frequencies in India:

• Annual (n=1) — some bonds and schemes.
• Half-yearly (n=2) — many bank FDs.
• Quarterly (n=4) — most bank savings and FDs.
• Monthly (n=12) — recurring deposits and some loans.
• Daily (n=365) — savings accounts technically compute daily.

More frequent compounding yields more interest for the same nominal rate.

Worked Example 1: Fixed Deposit of Rs 1,00,000 at 7% for 5 Years

Annual Compounding (n=1)

• A = 1,00,000 × (1 + 0.07/1)^(1×5)
• A = 1,00,000 × (1.07)^5
• A = 1,00,000 × 1.4026 = Rs 1,40,260
• Interest earned = Rs 40,260

Quarterly Compounding (n=4)

• A = 1,00,000 × (1 + 0.07/4)^(4×5)
• A = 1,00,000 × (1.0175)^20
• A = 1,00,000 × 1.4148 = Rs 1,41,480
• Interest earned = Rs 41,480

Quarterly compounding earns Rs 1,220 more — same rate, same tenure, only frequency differs.

Worked Example 2: Long-Term Investment of Rs 5,00,000 at 10% for 15 Years

• A = 5,00,000 × (1.10)^15
• A = 5,00,000 × 4.1772 = Rs 20,88,600
• Interest = Rs 15,88,600

Your money more than quadrupled. The interest (Rs 15.88 lakh) is over three times the principal — this is the power of compounding over long periods.

Worked Example 3: Monthly RD of Rs 5,000 at 6.5% for 5 Years

Total invested = 5,000 × 60 = Rs 3,00,000. Using the RD formula (which accounts for monthly compounding):

• M ≈ 3,00,000 × [(1.0054167)^60 − 1] / (1 − 1/1.0054167) ... simplified
• Maturity value ≈ Rs 3,55,400
• Interest ≈ Rs 55,400

Simple vs Compound Interest — A Comparison

On Rs 1,00,000 at 8% for 10 years:

• Simple interest: 1,00,000 × 0.08 × 10 = Rs 80,000 interest; total Rs 1,80,000
• Compound interest (annual): 1,00,000 × (1.08)^10 = 1,00,000 × 2.1589 = Rs 2,15,890; interest Rs 1,15,890

Compound interest produces Rs 35,890 more over 10 years. Over 30 years, the gap widens to several lakh rupees.

The Rule of 72 — Doubling Time

The Rule of 72 is a quick mental shortcut to estimate how long it takes to double your money:

Doubling Time (years) = 72 / Annual Rate (%)

• At 6%: 72/6 = 12 years to double
• At 8%: 72/8 = 9 years
• At 12%: 72/12 = 6 years
• At 15%: 72/15 = 4.8 years

This rule is remarkably accurate for rates between 6% and 10% and is a quick way to evaluate investment options.

Real-World Indian Examples

PPF at 7.1% for 15 Years

Rs 1,50,000 invested annually (approximated as lump sum at year start):

• A ≈ 1,50,000 × (1.071)^15 = 1,50,000 × 2.827 = Rs 4,24,050 after 15 years (single investment)
• Annual investments compound to roughly Rs 40 lakh if Rs 1.5 lakh is invested every year for 15 years.

See our PPF Calculator for the full picture.

SIP at 12% for 20 Years

Rs 10,000/month SIP compounding at 12%: future value ≈ Rs 99.9 lakh against total investment of Rs 24 lakh. Use our SIP Calculator to model this.

Frequently Asked Questions

What is the compound interest formula?

A = P × (1 + r/n)^(n×t), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

What is the difference between simple and compound interest?

Simple interest is calculated only on the original principal every period. Compound interest is calculated on the principal plus accumulated interest, so your money grows exponentially rather than linearly.

What is the Rule of 72?

The Rule of 72 estimates how long it takes to double your money. Divide 72 by the annual interest rate. At 8%, money doubles in 72/8 = 9 years. At 12%, it doubles in 6 years.

Conclusion

Compound interest is the foundation of wealth creation. The formula is simple, but the compounding frequency and time horizon make an enormous difference. Start early, let the compounding work, and let our Compound Interest Calculator, PPF Calculator, and SIP Calculator handle the maths for you.