# Simple and Compound Interest — Formulas, Differences and Shortcuts

Source: https://skills101.in/learn/aptitude/simple-and-compound-interest — Skills101 free tutorial (Quantitative Aptitude). Updated 2026-11-09.

When you put money in a bank (or borrow it), the extra money paid for using it is called **interest**.

- **Principal (P):** the money at the start
- **Rate (R):** % per year
- **Time (T):** in years
- **Amount (A):** principal + interest

## 1. Simple vs compound — the picture

![Bars for ₹1000 at 10%: simple interest adds ₹100 each year (1100, 1200, 1300) while compound interest gives 1100, 1210, 1331](https://skills101.in/learn-img/aptitude/si-vs-ci.svg)

- **Simple interest (SI):** interest is always on the **original** principal → the same amount every year.
- **Compound interest (CI):** each year's interest is added to the principal, so next year you earn **interest on interest**.

## 2. Simple interest

> **SI = P × R × T ÷ 100**     **A = P + SI**

### Example 1
*Find the SI on ₹8,000 at 6% per year for 3 years.*

SI = 8000 × 6 × 3 ÷ 100 = **₹1,440**. Amount = ₹9,440.

### Example 2
*At what rate will a sum double itself in 8 years at simple interest?*

Doubling means SI = P. So P = P × R × 8 ÷ 100 → R = 100 ÷ 8 = **12.5%**.

> **Shortcut:** at simple interest, money becomes n times in (n − 1) × 100 ÷ R years.

## 3. Compound interest

> **A = P × (1 + R/100)ᵀ**     **CI = A − P**

### Example 3
*Find the CI on ₹10,000 at 10% per year for 2 years.*

A = 10000 × 1.1 × 1.1 = 12,100. CI = **₹2,100**.

### Compounded half-yearly or quarterly

- Half-yearly: use **R/2** and **2T**
- Quarterly: use **R/4** and **4T**

### Example 4
*Find the amount on ₹20,000 at 10% per year compounded half-yearly for 1 year.*

Rate per half-year = 5%, number of periods = 2. A = 20000 × 1.05 × 1.05 = **₹22,050**.

## 4. The CI − SI shortcut (very common)

For the same P and R:

> **2 years: CI − SI = P × (R/100)²**
> **3 years: CI − SI = P × (R/100)² × (3 + R/100)**

### Example 5
*The difference between CI and SI on a sum for 2 years at 10% is ₹50. Find the sum.*

50 = P × (0.1)² = P × 0.01 → P = **₹5,000**.

Why it works: in year 2, CI also earns interest on year 1's interest (₹500 on ₹5,000 at 10% → ₹50 extra).

## 5. Percentage tricks for CI

Compound interest is just **successive percentage increase**. For 2 years at R%, the total growth is R + R + R²/100.

- 10% for 2 years → 10 + 10 + 1 = **21%**
- 20% for 2 years → 20 + 20 + 4 = **44%**

### Example 6
*A sum becomes ₹4,840 in 2 years at 10% compound interest. Find the sum.*

It grew by 21%, so P × 1.21 = 4840 → P = **₹4,000**.

### Example 7
*A sum doubles in 5 years at compound interest. In how many years will it become 8 times?*

8 = 2³, so it needs 3 doublings → 3 × 5 = **15 years**.

> **Rule of 72:** money roughly doubles in 72 ÷ R years at compound interest. At 8%, about 9 years.

## Common mistakes

- Using the CI formula for simple interest (or the other way round). Read the question.
- For half-yearly, forgetting to change **both** the rate (halve it) and the time (double it).
- Using CI − SI = P(R/100)² for 3 years. It is only for 2 years.

## Quick recap

- SI = PRT/100, same interest every year.
- A = P(1 + R/100)ᵀ for CI.
- CI − SI for 2 years = P(R/100)².
- 2 years of CI at R% = R + R + R²/100 % growth.
- If a sum becomes k times in t years (CI), it becomes kⁿ times in n × t years.


Practice quiz and free certificate: https://skills101.in/learn/aptitude/simple-and-compound-interest