## Simple Interest and Compound Interest

**Simple Interest
(SI) **

Principal: - The
money borrowed or lent out for certain period is called the principal or the
Sum.

Interest: - Extra
money paid for using other money is called interest.

If the interest on a
sum borrowed for certain period is reckoned uniformly, then it is called simple
interest.

Let Principal = P, Rate = r % per annum (p.a.), and Time = t years then

Simple Interest(SI)=
((P×r×t))/100

Using this formula we
can also find out

P=(100×SI)/(r×t);

r=(100×SI)/(P×t);

t=(100×SI)/(P×r).

**Compound Interest:**

When compound
interest is applied, interest is paid on both the original principal and on
earned interest.

So for one year
Simple interest and Compound interest both are equal.

Suppose if you make a
deposit into a bank account that pays compounded interest, you will receive
interest payments on the original amount that you deposited, as well as
additional interest payments.

This allows your
investment to grow even more than if you were paid only simple interest. So
Amount at the end of 1st year (or Period) will become the principal for the 2nd
year (or Period) and Amount at the end of 2nd year (or Period) becomes the
Principal of 3rd year.

Amount = Principal +
Interest

A= P (1+r/100)
^n

A= Amount,

P= Principal,

r= Rate %,

n= no. of years.

So Compound Interest
= [P (1+r/100) ^ n - P]

= P [(1+r/100) ^ n –
1]

**Condition:-**

**1.**When interest
is compounded annually,

Amount = P(1+r/100)^n

**2.**When interest
is compounded half yearly,

Amount =
P(1+(r/2)/100)^2n

**3.**When interest is
compounded Quarterly,

Amount
=P(1+(r/4)/100)^4n

**4.**When interest is
compounded annually but time is in fraction, say 3 whole 2/5 year

Amount =
P(1+r/100)^3×(1+(2r/5)/100)

**5.**When Rates are
different for different years, say r1%, r2%, and r3% for 1st, 2nd and 3rd year
respectively.

Then,

Amount =
P(1+r1/100)×(1+r2/100)×(1+r3/100).

Present worth of Rs.
x due n years hence is given by:

Present Worth =
x/(1+r/100)

**Difference between
Compound Interest & Simple interest Concept For Two years **

CI – SI =P(r/100)^2

For Three Year

CI – SI =P(r^2/(100^2
))×(300+r)/100)

For Two
year

**CI/SI=(200+r)/200**

**Quant
Quiz for Simple Interest & Compound Interest **

**1. A sum of money at
simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The
sum is:**

A) Rs. 720

B) Rs. 698

C) Rs. 678

D) Rs. 696

E) none of these

**2. A sum fetched a
total simple interest of Rs. 4016.25 at the rate of 9 % p.a. in 5 years. What
is the sum?**

A) Rs. 8045

B) Rs. 8925

C) Rs. 8900

D) Rs. 8032.45

E) none of these

**3. A sum of money
amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate
of simple interest. The rate of interest per annum is:**

A) 12 %

B) 13 %

C) 8 %

D) 12.5 %

**4. A person borrows
Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to
another person at 6.25% p.a. for 2 years.Find his gain in the transaction per
year.**

A) Rs. 112.50

B) Rs. 175

C) Rs.
150

D) Rs. 125.50

**5. A man took loan
from a bank at the rate of 12% p.a. simple interest. After 3 years he had to
pay Rs. 5400 interest only for the period.The principal amount borrowed by him
was**:

A) Rs. 12000

B) Rs.15000

C) Rs.
12500

D) Rs. 22000

**6.How much time will
it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum
of simple interest?**

A)3 year

B)4 year

C)5 year

D)6 year

**7. Bhavika
took a loan of Rs. 1200 with simple interest for as many years as the
rate of interest.If she paid Rs. 432 as interest at the end of the loan period,
what was the rate of interest?**

A)3.6

B) 5

C) 6

D)25

**8. A lent Rs. 5000 to
B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate
of interest and received Rs. 2200 in all from both of them as interest. The
rate of interest per annum is:**

A) 5 %

B) 7%

C)10 %

D) 12%

9.**A bank offers 5%
compound interest calculated on half-yearly basis. A customer deposits Rs. 1600
each on 1st January and 1st July of a year. **

**At the end of the
year, the amount he would have gained by way of interest is:**

A)123

B) 122

C)121

D)120

**10.The compound
interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is:**

A)2.5

B) 2

C) 3

D) 4

E) none of these

**11.At what rate of
compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2
years?**

A)8 %

B) 9%

C) 6 %

D) 8.5 %

E) none of these

**12.The difference
between simple interest and compound on Rs. 1200 for one year at 10% per annum
reckoned half-yearly is:**

A)Rs. 3

B) Rs. 4

C) Rs. 3.5

D) Rs. 7.5

E) none of these

**13.The least number
of complete years in which a sum of money put out at 20% compound interest will
be more than doubled is:**

A) 4

B) 5

C) 6

D) 2.5

E) none of these

**14.What will be the
compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12
p.c.p.a.?**

A) Rs.10123.20

B) Rs. 9000

C) Rs. 12000

D) Rs. 10163.34

E) none of these

**15.Simple interest on
a certain sum of money for 3 years at 8% per annum is half the compound
interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on
simple interest is:**

A)Rs. 1650

B)Rs. 2000

C)Rs. 1750

D) Rs.1550

E) none of these

**Answers with
Explanation:**

Anwers:

1.B

2.B

3.A

4.A

5.B

6.B

7.C

8.C

9.C

10.B

11.C

12.A

13.A

14.A

15.C