Today I am going to share Simple Interest and Compound Interest tricks and shortcuts.

###

## Simple Interest

### Examples

### #1

**Find the simple interest, If**

- P = Rs.1000, R = 20% per annum, T = 4 years.
- P = Rs.600, R = 5% per annum, T = 4 months.
- P = Rs.200, R = 6% per six months, T = 3 years.
- P = Rs.500, R = 2% per six months, T =
^{5}/_{2}years. - P = Rs.400, R = 3% per three months, T = 2 months.
- P = Rs.730, R = 10% per annum, T = 120 days.
- P = Rs. 3000, R = 61/4 per annum, T = period from 4th Feb to 18th Apr.

### # Solution

**4×20×10 ⇒ 800****2×5 = 10**

**6×2×3×2 = 72****5×2×5=50****4×2=8****73/3=24****37.50**

### #2

**Find the following:**

- P = Rs. 100, R = 3% per annum, T = 2 year, A= ?
- P = Rs. 500, R = 6% per annum, T = 4 months, A= ?
- P = Rs. 400, R = 3.65% per annum, T = 150 days, A= ?
- A = Rs. 540, S.I = Rs. 108 , R = 5%, T = ?
- A = Rs. 1,120, R = 5%, T = 2
^{2}/_{5}yr, S.I = ?

### # Solution:

**S.I = 6 ; A = S.I + principal ; A = 6 + 100 ⇒ 106****S.I = 10 ; A = S.I + P ; A = 10+500 ⇒ 510****S.I = 6 ; A = 400 + 6 ⇒ 406****T = 5 yr.**

**120**

### #3

- A sum of money lent out at simple interest amounts to Rs. 720 after 2 years and to Rs. 1020 after a further period of 5 years. Find the sum and the rate %.
- Adam borrowed some money at the rate of 6% p.a. for the first two years, at the rate of 9% p.a. for the next three years, and at the rate of 14% p.a. for the period beyond five years. If he pays a total interest of Rs. 11,400 at the end of nine years , how much money did he borrow ?
**(Bank P.O 1999)** - A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6
^{1}/_{4}% p.a. for 2 years. Find his gain in the transaction per year.**(S.S.C.2000)** - A certain sum of money amounts to Rs. 1008 in 2 years and to Rs. 1164 in 3
^{1}/2 years.Find the sum and the rate of interest? - The simple interest on a certain sum of money for 2
^{1}/2 years at 12% per annum is Rs. 40 less than the simple interest on the same sum for 3^{1}/2 years at 10% per annum. Find the sum.

### # Solution

**Principal = 600, R = 10%****12000****112.50**

**[ 1164-1008 = 156 ]****⇒**^{156}/_{3×4}= 208 ; R =^{208}/_{2×800}×100**⇒**13^{7x}/_{20}-^{3x}/_{10}= 40**⇒ x = ( 40****× 20 )****⇒ x = 800 [ Hint : Given Below ]**

## # Compound Interest

### Trick :

#### Calculating Compound Interest for 3 Years

#### Calculating Compound Interest for 4 year

### # Formulas

**Case 1.**When interest is not Compound yearly,

Amount after 't' years A = P [1+

n= no of compounding per year^{r}/_{n}_{×}_{100}]^{nt}
When interest is compounded half yearly, n = 2

compounded quarterly, n = 4

compounded monthly, n = 12

**Case 2**. When rate % is no equal every year and interest is compounded yearly

Basic formula :

P [1+

But as rate % is not same every year, so

A = P [1+

Where R1 = Rate% p.a. for t1 years. and R2 = Rate % p.a. for t2 years.

T = 5

A= (whole part) × (fraction part of time )

P [1+

^{r}/_{100}] [1+^{r}/_{100}] ...upto 't' timesBut as rate % is not same every year, so

A = P [1+

^{r1}/_{100}]^{t1 }[1+^{r2}/_{100}]^{t2 }.... and so onWhere R1 = Rate% p.a. for t1 years. and R2 = Rate % p.a. for t2 years.

**Case 3**When interest is compounded yearly but time is in fractionT = 5

^{3}/_{4 years}A= (whole part) × (fraction part of time )

_{ }A = P [1+^{r}/_{100}]^{5 }× [1+^{3r/4/100}]### # Difference between Compound Interest and Simple Interest

CI - SI = P [ R/100 ]2

When time t = 3 years

CI - SI = P [ (

^{R}/100^{3 }+3 (^{R}/100)^{2}]### # Examples

### #1

- If the compound interest on a certain sum for two years at 10% p.a. is Rs 2,100 the simple interest on it at the same rate for two years will be.
**( RRB, 2009)** - The compound interest on a sum for 2 years is Rs. 832 and the simple interest on the same sum for the same period is Rs. 800. The difference between the compound and simple interest for 3 years will be.
- The difference between simple interest and compound interest on a sum for 2 years at 8% when the interest is compounded annually is Rs. 16, if the interest were compounded half yearly, the difference in one interest would be nearly.
- The difference in C.I and S.I for 2 years on a sum of money is Rs. 160.If the S.I for 2 years be Rs. 2880, the rate of percent is .

###
**# Solution**

**1. 2000**

**2. 98.56**

3.

**04**
4.

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