Compound Interest Formula & Calculation Guide

Compound Interest Defined

Compound interest earns interest on both principal and previously accumulated interest. Money grows faster than simple interest because each period’s interest becomes part of the next period’s base.

Formula:

A = P(1 + r/n)^(nt)

• A = Final amount
• P = Principal
• r = Annual interest rate (as decimal: 8% = 0.08)
• n = Compounding periods per year
• t = Time in years
• CI = A − P

Compounding Frequencies

Frequency	n
Annually	1
Half-yearly	2
Quarterly	4
Monthly	12

Higher n → slightly higher A for the same annual rate.

Example 1: Annual Compounding

P = ₹1,00,000, r = 10%, t = 3 years, n = 1

A = 100000 × (1.10)³ = 100000 × 1.331 = ₹1,33,100

CI = ₹33,100

Example 2: Quarterly Compounding

Same P, r, t but n = 4: rate per quarter = 10%/4 = 2.5%

A = 100000 × (1.025)^12 = ₹1,34,489 (higher than annual)

Example 3: Compare with Simple Interest

SI for same terms = ₹30,000. CI = ₹33,100 — the ₹3,100 difference is interest-on-interest.

Rule of 72 (Quick Estimate)

Years to double ≈ 72 / interest rate. At 12% p.a., money doubles in ~6 years.

Real Applications

• Fixed deposits and recurring deposits
• Mutual fund long-term projections (approximate)
• Inflation impact on purchasing power
• Loan comparisons (effective annual rate)

Use the Compound Interest Calculator for year-wise breakdown tables.

Frequently Asked Questions

What is effective annual rate (EAR)?

EAR accounts for compounding frequency — compares products fairly.

Is compound interest used for credit cards?

Credit card interest typically compounds daily on outstanding balance — very expensive if unpaid.

Can I use percentage instead of decimal for r?

In the standard formula, r must be decimal (0.08 not 8). Our calculator accepts percentage input.

What is continuous compounding?

Limit as n→∞: A = Pe^(rt). Used in advanced finance, rarely in retail banking.

How does CI relate to EMI?

EMI loans use reducing balance — different math. See EMI Calculation Guide.