__CHAPTER-5__

__SIMPLE INTEREST AND COMPOUND INTEREST__

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__What is Interest?__

When borrowed some money from other for the personal or commercial purpose we pay some additional money to him after a certain period of time is called **Interest**.

__What is Simple Interest?__

**Simple interest** is calculated only on the principal amount, or on that portion of the principal amount that remains.

__What is Compound Interest?__

**Compound interest** is interest added to the principal of a deposit or loan so that the added interest also earns interest from then on. This addition of interest to the principal is called *compounding*.

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__What is Principle?__

The money borrowed for a certain time period called **Principle or Sum****.**

__What is Amount?__

The Addition of Simple Interest and Principle is called the** ****Amount.**

**A = S.I + P (Principle).**

**S.I = A (Amount) – P (Principle).**

__What is per annum means?__

Per annul means for a year.

**P = Principle**, **R = Rate of per annum**, **T = Number of years**

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__Formulas Need to Remember__

**S.I** **= **

**P**** = **

** **

**R** =

__Example:__

Find the simple interest on Rs 400 for 4 years at 4 per cent ?

__Answer:__

SI = 400 x 4 x 4 / 100

Simple interest in 4 years is Rs 64 .

** Example:** Find the Simple Interest on Rs. 40000 at 25 / 4 % per annul for the period from 4th January, 2013 to 18th march, 2013.

__Answer:__

Step 1: First we calculate the period of time taken that is = January = (31 – 4) = 27 days, February = 28 days, March = 18 day. Add all together (27 + 28 + 18 ) = 73 / 365 year = 1 / 5 years.

Step 2: we know Principle P = 40000, and R = 25 / 4 % p.a.

Step 3: S.I = Rs. ( 40000 X 25 X 1 X 1 / 4 X 100 X 5 ) = Rs. 500

So the S.I is 500.

__Example:__

What is the rate of p.c.p.a ? If the simple interest accrued on amount of Rs.25500 at the end of 3 years is 9180.

__Answer:__

we know the formula is S.I = PRT / 100

So, S.I = 9180 , P = 25500 , T = 3 years , R = ?

9180 = 25500 x R x 3 / 100

R = 9180 / 765 = 12 %

so, rate of p.c.p.a = 12 %

__Example:____ __

Sarikatakes a sum from Dinesh at simple interest at 25x / 2 per annul and amounts to Rs.3202.50after 6 years. Find the Sum or Principle taken by Sarika from Dinesh.

__Answer:__

First We consider sum is x and Rate percent is 25x / 2 and Time is 6 years, So

**Step 1:**Then **S.I. = Rs. P X R X T / 100 = 3x / 4.**

**Step 2:** Amount = Sum + Simple Interest = x + 3x / 4 = **7x / 4.**

**Step 3:** 7x / 4 = 3202.50 and x = 3202.50 X 4 / 7 = **1830.**

Sarika taken sum from Dinesh is **1830.**

__Some important formulae of Compound Interest__

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**Type I:**** When interest compounded yearly :** **A = P ( 1 + r / 100 ) ^{n}**

**Type II:**** When interest compounded half – yearly :**

Amount = **P [ 1 + r / 2 / 100 ] ^{4n}** or = P =

**[ 1 + r / 200 ]**

^{2n}

**Type III:**** When interest compounded quarterly :**

Amount = **P [ 1 + r / 4 / 100 ]** or = **P [ 1 + r / 400 ]** ^{4n}

^{ }

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__Example:__

Principle is 15000 at rate percent 4% p.c.p.a for 2 years, and compound annually

Find the C.I.

__Answer:__

We apply the formula to obtain C.I that is **C.I = p [(1 + r / 100) ^{n}**

**– 1]**

**P = 15000.**

**R = 4%.**

**Time = 2 years.**

= 15000 x [( 1 + 4 / 100)

^{2}– 1].

= 15000 x [26×26/25×25 – 1]. [ as we put down (26 / 25)

^{2}]

= 15000 x 51 / 625 .

**=**

**1224**

__Example:__

The Simple Interest accrued on an amount of Rs.22,500 at the end of 3 years is Rs. 10800what would be the Compound Interest accrued on the same amount at the same rate at the end of two years ?

__Answer:__

Here is given **amount = 22,500** , **Time = Years 3** and **S.I = 10800** so we need to find Rate percent.

**Step 1:** we know S.I = P x R x T / 100

10,800 = 22,500 x R x 3 / 100

R = 1080000 / 67500 = 16 % So R = 16 %.

**Step 2:** Compound Interest accrued on the **same amount** at the **same rate** at the **end of two years**

is we apply the formula

C.I = 22500 x (116 / 100 x 116 / 100 – 1 )

= 22500 x( 116 x 116/ 10000 – 1) = 22500 x( 13456 / 1000) – 1 = 22500 x (1.3456 – 1) = 22500 x 0.3456 =7776

So the C.I end of two years is 7776.