Simple Interest vs Compound Interest — Formula and Examples

Introduction

Simple interest and compound interest are two methods of calculating interest on money — whether you’re borrowing a loan or growing savings. Understanding the difference is essential for students studying mathematics or commerce, professionals comparing loan offers, and anyone making financial decisions.

This guide explains both types with clear formulas, worked examples, and a comparison to help you choose the right calculator for your needs.

Simple Interest (SI)

Definition

Simple interest is calculated only on the original principal amount. The interest remains the same every year regardless of how long the money is invested or borrowed.

Formula

SI = (P × R × T) / 100

Where:

• P = Principal (initial amount in ₹)
• R = Rate of interest per annum (%)
• T = Time period (in years)

Total Amount = P + SI

Example 1: ₹50,000 at 8% for 3 years

SI = (50,000 × 8 × 3) / 100 = ₹12,000

Total Amount = 50,000 + 12,000 = ₹62,000

Example 2: ₹1,00,000 at 10% for 6 months

T = 6/12 = 0.5 years

SI = (1,00,000 × 10 × 0.5) / 100 = ₹5,000

Characteristics of Simple Interest

• Interest is constant each year
• Growth is linear (straight line on a graph)
• Used in short-term loans, some FDs, and exam problems
• Simpler to calculate manually

Compound Interest (CI)

Definition

Compound interest is calculated on the principal plus any previously accumulated interest. Interest earns interest — this is the “compounding” effect.

Formula

A = P × (1 + r/n)^(n×t)

CI = A − P

Where:

• A = Final amount
• P = Principal
• r = Annual interest rate (as decimal, e.g., 10% = 0.10)
• n = Number of times interest compounds per year
• t = Time in years

Compounding Frequencies

Frequency	n value
Annually	1
Half-yearly	2
Quarterly	4
Monthly	12
Daily	365

Example 1: ₹1,00,000 at 10% compounded annually for 3 years

A = 1,00,000 × (1 + 0.10/1)^(1×3) A = 1,00,000 × (1.10)³ A = 1,00,000 × 1.331 = ₹1,33,100

CI = 1,33,100 − 1,00,000 = ₹33,100

Compare: SI for the same would be ₹30,000. CI earns ₹3,100 more due to compounding.

Example 2: ₹2,00,000 at 12% compounded quarterly for 2 years

r = 0.12, n = 4, t = 2

A = 2,00,000 × (1 + 0.12/4)^(4×2) A = 2,00,000 × (1.03)⁸ A = 2,00,000 × 1.2668 = ₹2,53,360

CI = ₹53,360

Side-by-Side Comparison

Feature	Simple Interest	Compound Interest
Calculated on	Principal only	Principal + accumulated interest
Growth pattern	Linear	Exponential
Formula	P×R×T/100	P(1+r/n)^(nt) − P
Better for borrower	CI is lower for short terms	SI is lower for long terms
Better for investor	SI gives less returns	CI gives more returns
Common usage	Short-term loans, simple FDs	Savings accounts, mutual funds, long-term loans

Year-by-Year Comparison: ₹10,000 at 10%

Year	SI Interest (Total)	CI Interest (Total)	Difference
1	₹1,000	₹1,000	₹0
2	₹2,000	₹2,100	₹100
3	₹3,000	₹3,310	₹310
5	₹5,000	₹6,105	₹1,105
10	₹10,000	₹15,937	₹5,937

The longer the duration, the greater the advantage of compound interest for investors (and the greater the cost for borrowers).

When to Use Which

Use Simple Interest when:

• Calculating short-term loan payments
• Solving school/college math problems
• Quick mental estimates

Use Compound Interest when:

• Comparing bank FD or savings account returns
• Planning mutual fund or SIP growth
• Calculating long-term loan costs (EMI uses compound)
• Projecting retirement savings

Try It Online

• Simple Interest Calculator — instant SI calculation with formula display
• Compound Interest Calculator — supports multiple compounding frequencies with year-by-year table

Both tools on Numverto are free, show step-by-step working, and use Indian rupee formatting.

Frequently Asked Questions

Which gives more return — simple or compound interest?

Compound interest always gives more return than simple interest for the same rate and duration (beyond year 1), because you earn interest on accumulated interest.

Do Indian banks use simple or compound interest?

Most Indian banks use compound interest for savings accounts (quarterly compounding) and loans (monthly compounding via EMI). Simple interest is rarely used except in some short-term instruments.

What happens if compounding frequency increases?

More frequent compounding (monthly vs yearly) yields slightly higher returns because interest is added to principal more often. The difference is small for short periods but significant over many years.

Is EMI based on simple or compound interest?

EMI uses compound interest with monthly compounding (reducing balance method). Each month, interest is calculated on the remaining outstanding principal, not the original loan amount.

How do I calculate CI for half-yearly compounding?

Use n=2 in the formula. For ₹1 lakh at 10% for 1 year compounded half-yearly: A = 1,00,000 × (1 + 0.05)² = 1,00,000 × 1.1025 = ₹1,10,250. CI = ₹10,250 (vs ₹10,000 with annual compounding).