CAT 2026 Simple Interest and Compound Interest: Formulas, Shortcuts & Practice Questions

CAT Simple Interest Formulas

The key SI formulas for CAT cover interest, amount, principal, rate and time.

• Simple Interest: $SI = \frac{P \times R \times T}{100}$

• Amount: $A = P + SI = P\left(1 + \frac{RT}{100}\right)$

• Principal: $P = \frac{100 \times SI}{R \times T}$

• Rate: $R = \frac{100 \times SI}{P \times T}$

• Time: $T = \frac{100 \times SI}{P \times R}$

CAT Compound Interest Formulas

For CI, the compounding period determines the number of growth cycles.

- Compound Amount: $A = P\left(1 + \frac{R}{100}\right)^T$

- Compound Interest: $CI = A - P = P\left[\left(1 + \frac{R}{100}\right)^T - 1\right]$

- Depreciation: $A = P\left(1 - \frac{R}{100}\right)^T$

CAT 2026 SI and CI Important Shortcuts

Several standard shortcuts can reduce calculation time in CAT.

Difference Between CI and SI for 2 Years

For a principal $P$ and rate $R$:

$CI - SI = P\left(\frac{R}{100}\right)^2$

or $CI - SI = \frac{PR^2}{10000}$

For example, if $P = \text{₹}20,000$ and $R = 10\%$:

$CI - SI = 20000 \times \frac{10^2}{10000} = \text{₹}200$

Difference Between CI and SI for 3 Years

$CI-SI=P\left[3\left(\frac{R}{100}\right)^2+\left(\frac{R}{100}\right)^3\right]$

This formula is useful when a question directly asks for the difference between compound and simple interest over three years.

Half-Yearly Compounding

For half-yearly compounding, halve the rate and double the number of periods:

$A=P\left(1+\frac{R}{200}\right)^{2T}$

Quarterly Compounding

For quarterly compounding, divide the rate by 4 and multiply the periods by 4:

$A=P\left(1+\frac{R}{400}\right)^{4T}$

Different Interest Rates

If different rates apply during different periods:

$A=P\left(1+\frac{R_1}{100}\right)^{T_1}\left(1+\frac{R_2}{100}\right)^{T_2}$

CAT SI and CI Percentage Shortcuts

Percentage-based shortcuts are particularly useful in CAT questions involving repeated increases or decreases.

Successive Percentage Increase

If a value increases by a and then by b, the total percentage increase is:

$a+b+\frac{ab}{100}$

Increase Followed by Decrease

If a value increases by a and then decreases by b, the net percentage change is: $a-b-\frac{ab}{100}$

For equal increases and decreases of a%, the overall change is: −$\frac{a^2}{100}$

CAT 2026 Simple Interest and Compound Interest Practice Questions

Practise CAT-level Simple Interest and Compound Interest questions to strengthen formula application, calculation speed and accuracy.

1. The compound interest on a sum for two years at 20% per annum is ₹2,640. Find the simple interest on the same sum for three years at 15% per annum.
A. ₹2,700
B. ₹3,000
C. ₹3,300
D. ₹3,600

2. A sum of money amounts to ₹8,400 in 2 years and ₹9,240 in 4 years at simple interest. Find the principal.

A. ₹7,200
B. ₹7,560
C. ₹7,800
D. ₹8,000

3. A sum of Rs 10,000 is invested at 10% per annum compound interest for two years. What is the difference between the compound interest and simple interest?

A. Rs 90

B. Rs 100

C. Rs 110

D. Rs 120

4. A sum is invested at 20% per annum, compounded half-yearly, for 1.5 years. If the principal is Rs 10,000, what is the amount?

A. Rs 13,310

B. Rs 13,200

C. Rs 13,420

D. Rs 13,500

5. A machine depreciates by 10% in the first year and 20% in the second year. If its initial value is Rs 50,000, what is its value after two years?

A. Rs 36,000

B. Rs 36,500

C. Rs 37,000

D. Rs 38,000

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CAT 2026 SI and CI Important Question Types

These question types cover the common SI and CI approaches tested in CAT.

Recognising the question type quickly can help candidates choose the right formula and save valuable time in CAT 2026.

Common Mistakes in CAT SI and CI Questions

Small interpretation errors can lead to incorrect answers even when the calculation is straightforward.

• Using the SI formula when interest is compounded.

• Forgetting to halve the rate for half-yearly compounding.

• Forgetting to double the number of periods for half-yearly compounding.

• Treating successive percentage changes as simple addition.

• Confusing the final amount with the interest earned.

• Applying the 2-year SI-CI shortcut to a question involving three or more years.

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CAT 2026 SI and CI Quick Revision Formula Sheet

This quick revision sheet brings together the key SI and CI formulas needed for fast CAT 2026 revision.

Candidates can use these formulas to revise core concepts and solve SI and CI questions more efficiently.

Access a concise collection of important CAT Quant formulas for quick revision and efficient problem-solving.

Download now: CAT Important Formulas PDF

CAT 2026 SI and CI Preparation Strategy

A focused revision plan can make this topic easier to manage alongside the rest of Arithmetic.

Candidates should maintain an error log while practising. Recording the formula or calculation step responsible for each mistake can make revision more targeted.

CAT 2026 Mock Test

The CAT 2026 Free Mock Test gives candidates an opportunity to practise questions based on the actual exam format. Regular mock practice can help assess CAT preparation levels and improve time management.

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How to Identify the Right SI or CI Formula in CAT