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**www.tnpsc.academy – TNPSC APTITUDE AND MENTAL ABILITY – for Group 1, Group 2, Group 2A, Group 3, Group 4, VAO and Others.**

**COMPOUND INTEREST | tnpsc maths**

### FORMULAE :

### A = P [1 + (R / 100)]T

**Where, **

** A = Amount**

** P = Principal**

** R = Rate of interest**

** T = Time period**

#### Example :

What will be the compound interest on a sum of 50000 after 3 years at the rate of 12 % p.a?

*Solution :*

P = 50000, R = 12 %, n = 3 yr

A = P [1 + (R / 100)]T

= 50000 [1 + (12 / 100)]2

= 50000 [(28 / 25) * (28 / 25) * (28 / 25)]

= 3551232 / 5

= 70246.40

**Answer => 70246.40**

**Note :**

If the rate of interest for 1st year is r1 %, for 2nd year it is r2 % and for 3rd year it is r3 % then the amount for 3 years?

= P * [1 + (r1 / 100)] [1 + (r2 / 100)] [1 + (r3 / 100)]

**Note :**

#### Example :

The population of particular Area A of the city is 5000, it increases by 10 % in 1st year, and it is decreased by 20 % in the 2nd year because of some reason. In the 3rd year population increases 30 %, what will be the population of Area A at the end of the 3rd year?

**Solution :**

P =5000, R1 = 10 %, R2 = -20 %, R3 = 30 %

Population of area = P * [1 + (R1 / 100)] [1 + (R2 / 100)] [1 + (R3 / 100)]

= 5000 * [1 + (10 / 100)] [1 – (20 / 100)] [1 + (30 / 100)]

= 5000 * [11 / 10] [4 / 5] [13 / 10]

= 10 * 11 * 4 * 13

= 5720

**Answer => 5720**

**Note :**

Population after “n” yrs = P [1 + (R / 100)]n

Population n year ago = {P / [1 + (R / 100)]n}

**Note :**

#### Example :

The population of a city increases at the rate of 15 % p.a. If its population was 4000 at the end of year 2013, then what will be its population at the end of the year 2015?

**Solution :**

R = 15 %, n = 2 year, P = 4000

Population after 2 year = 4000 * [1 + (15 / 100)]2

= 4000 * [(23 / 20) * (23 / 20)]

= 10 * 529

= 5290

**Answer => 5290**

#### Example :

The population of a city increases at the rate of 5 % p.a. If the present population of the city is 370440, then what was its population 3 years ago?

**Solution :**

P = 370440, R = 5 %, n = 3 year

Population 3 years ago = {P / [1 + (R / 100)]n }

= {370440 / [1 + (5 / 100)3]}

= 370440 / [21 / 20]3

= (370440 * 8000) / (9261)

= 40 * 8000

= 320000

**Answer => 320000**

**Note :**

**Shortcut method for calculating compound interest :**

**Note :**

**Shortcut method for calculating compound interest :**

= [x + y + (xy / 100)] % of P

Let R = 10 % for 2 year,

= 10 + 10 + [(10 * 10) / 100]

= 20 + 1

= 21 % of P

**Answer => 21 % of P**

**Note :**

If a certain sum at Compound interest becomes A1 in “n” year and A2 in (n + 1) year, then

**Note :**

### Rate of CI = [(A2 – A1) / A1] * 100

Sum = [A1 * (A1 / A2)n]

#### Example :

A sum of money invested at compound interest amounts to 800 in 2 yr and 840 in 3 year. Find the rate of interest per annum and Sum?

**Solution :**

SI on 800 for 1 year = 840 – 800 = 40

SI = PRT / 100 = 40

= (800 * R * 1) / 100

R = 5 %

Amount = Sum [1 + (R / 100)]T

800 = x [1 + (5 / 100)]2

800 = (105 / 100) * (105 / 100) * (x)

800 = (21 / 20) * (21 / 20) * (x)

x = (800 * 20 * 20) / (21 * 21)

x = 320000 / 441

x = 725.62

**Another method :**

A1 = 800 , A2 = 840

Rate of CI = [(A2 – A1) / A1] * 100 %

= [(840 – 800) / 800] * 100 %

= 40 / 8 %

= 5 %

Sum = [A1 (A1 / A2)n]

= [800 (800 / 840)2]

= 800 * (800 / 840) * (800 / 840)

= 320000 / 441

Sum = 725.62

**Note :**

If the difference between the SI & CI on the same amount at “R %” for “2” year,

= P [r / 100]2

And if the difference between the SI and CI on the same amount at r % for 3 year,

= P [r2 / 1002] [3 + (r / 100)]

**Note :**

#### Example :

If the difference between the CI and SI on a certain sum for 2 year at 8 % per annum is 32, then the sum?

**Solution :**

n = 2 , R = 8 % , Difference = 32

Difference = P [r / 100]2

32 = p [82 / 1002]

P = (32 * 100 * 100) / (8 * 8)

P = 5000

**Answer => 5000**

#### Example :

If the difference between CI and SI on 1000 for 3 year at 5 % p.a

**Solution :**

P = 1000 , R = 5 %

= P [r2 / 1002] [3 + (r / 100)]

= 1000 [(5 *5) / (100 * 100)] [3 + (5 / 100)]

= 76.25

*Answer = > 76.25*

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Good Explanation,but some bracket issue is there in formulae, Please continue your support.

Thanks,

Rajmohan.M

When u post other aptitude and mental ability prblms?

We are preparing for all topics. Will be updated soon.

good Explanation thank you.