Simple Interest and Compound Interest – MBA CUET PG – Notes & Practice Questions

Simple Interest

Basic Definitions:

• Principal (P): Initial amount of money.

• Rate (R): Rate of interest per annum (in %).

• Time (T): Time period in years.

• Simple Interest (SI): Interest calculated only on the principal.

• Amount (A): Total sum after interest.

Fundamental Formulas:

(a) Simple Interest

$$SI=\frac{P\times R\times T}{\mathrm{100<span\; style="font-size:\; 16px;\; font-family:\; Georgia,\; \text{'}Times\; New\; Roman\text{'},\; \text{'}Bitstream\; Charter\text{'},\; Times,\; serif;"></span>}}$$

(b) Amount

$$A = P + SI$$

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

Reverse Formulas:

(a) To Find Principal

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

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(b) To Find Rate

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

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(c) To Find Time

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

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Key Properties of SI:

• Interest remains constant every year.

• Total SI for n years:

$$SI_n = n \times SI_1$$

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• SI does not depend on compounding; it is linear.

Compound Interest

Definitions:

Compound interest is calculated on principal plus accumulated interest from previous periods.

Annual Compounding:

(a) Amount

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

(b) Compound Interest

$$CI = A – P$$

Half-Yearly Compounding:

• Rate becomes \(\fracR2\) per half-year

• Time becomes 2T half-years

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

$$CI = A – P$$

Quarterly Compounding:

• Rate becomes \(\fracR4\)

• Time becomes 4T

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

$$CI = A – P$$

Monthly Compounding:

• Rate becomes \(\fracR{12}\)​

• Time becomes 12T

$$A = P\left(1 + \frac{R}{1200}\right)^{12T}$$

General Compounding Formula:

If interest is compounded

$n$

n times per year:

$$A = P\left(1 + \frac{R}{100n}\right)^{nT}$$

Difference Between CI and SI

For two years:

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

For three years:

$$CI – SI = P\left[ \left(1 + \frac{R}{100}\right)^3 – 1 – \frac{3R}{100} \right]$$

Depreciation Formula (Value decreases)

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

Population Growth Formula

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

Population decrease:

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

Short Tricks

For Simple Interest

1. SI percent for T years

If rate = R% 

$\mathrm{<span\; class="mord"\; style="font-size:\; 16px;\; font-family:\; Georgia,\; \text{'}Times\; New\; Roman\text{'},\; \text{'}Bitstream\; Charter\text{'},\; Times,\; serif;"><span\; style="font-size:\; 16px;">per\; annum\; for \; T </span></span>}$

$\mathrm{<span\; class="katex"\; style="font-size:\; 16px;\; font-family:\; Georgia,\; \text{'}Times\; New\; Roman\text{'},\; \text{'}Bitstream\; Charter\text{'},\; Times,\; serif;"><span\; style="font-size:\; 16px;">years:</span></span>}$

Total % interest =

$$RT\mathrm{\%}$$

(Useful to find SI directly when P is given.)

2. If SI for 2 years and 3 years is given

Difference = SI for 1 year.

Since SI is same every year:

$$S{I}_{1year}=S{I}_3-S{I}_{\mathrm{2<span\; style="font-size:\; 16px;\; font-family:\; Georgia,\; \text{'}Times\; New\; Roman\text{'},\; \text{'}Bitstream\; Charter\text{'},\; Times,\; serif;"></span>}}$$

3. When amount becomes k times

If Amount = k × Principal in SI:

$$RT = (k – 1) \times 100$$

Use to find time or rate quickly.

Example: Amount becomes 1.4 times →

$$RT = 40$$

4. Finding Time when SI is a fraction of P

If

$SI = \frac{P}{n}$

​

$$RT = \frac{100}{n}$$

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5. To find Rate quickly

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

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To solve faster:
Reduce fraction → approximate quickly.

Short Tricks for Compound Interest

1. Difference between CI and SI for 2 years

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

Use this to avoid full calculations.

2. Percentage growth shortcut (CI for 2 years)

If something grows by R% for 2 years, total growth %:

$$R + R + \frac{R^2}{100}$$

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Example: 10% yearly for 2 years
Total =

$10 + 10 + 1 = 21\%$

3. Percentage growth for 3 years

$$\text{Total \%} = 3R + 3\frac{R^2}{100} + \frac{R^3}{10000}$$

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4. Successive Percentage Formula (compound %)

If rate changes year-wise (e.g., 10%, then 20%, then 5%):

Total % change =

$$a + b + c + \frac{ab}{100} + \frac{ac}{100} + \frac{bc}{100} + \frac{abc}{10000}$$

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5. Amount becomes k times (CI)

To find rate:

$${(1+\frac{R}{100})}^T=k$$

For small T (like 2 or 3 years), expand:

For 2 years:

$$k=1+\frac{2R}{100}+\frac{R^2}{\mathrm{10000<span\; style="font-size:\; 16px;\; font-family:\; Georgia,\; \text{'}Times\; New\; Roman\text{'},\; \text{'}Bitstream\; Charter\text{'},\; Times,\; serif;"></span>}}$$

6. Population/increase-decrease quick trick

If population increases by R% per year for T years:

$$\text{Multiplier} = \left(1 + \frac{R}{100}\right)^T$$

If decreases:

$$\left(1 – \frac{R}{100}\right)^T$$

Use binomial expansion only if needed for small T.

7. Half-yearly & Quarterly quick check

• Half-yearly → Rate becomes \(​, time

  $2T$

  2T

• Quarterly →
  Rate becomes

  $\frac{R}{4}$

  4R​, time

  $4T$

  4T

Compute mentally by adjusting the rate and time.

8. CI for small rates (approximation trick)

For small R (<10%),

$$CI \approx SI + \frac{P R^2 T (T-1)}{20000}$$

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Very handy in options-based questions.