**SIMPLE AND COMPOUND INTEREST**
** **

Interest is defined as the cost of borrowing money as in the case of interest charged on a loan balance. Conversely, interest can also be the rate paid for money on deposit as in the case of a certificate of deposit. Interest can be calculated in two ways, Simple interest or Compound interest.

** Simple interest is calculated on the principal or original amount of a loan **
or deposit.

** Compound interest is calculated on the principal amount and also on the **
accumulated interest of previous periods, and can thus be regarded as
"interest on interest."

### SIMPLE INTEREST:

** If A stands for Amount; P stands for Principal; S.I stands for **
**Simple Interest; T stands for Time (in years); R stands for Rate per cent per year **
(per annum), then

### COMPOUND INTEREST:

** If A stands for Amount; P stands for Principal; C.I stands for **
**Compound Interest; n stands for Time (in years); R stands for Rate per cent per **
year (per annum), then

1) A = P(1 + 𝑅

100) n

2) C.I = A – P

If interest is compounded annually but time is in fraction, (Suppose time =
21
5 years), then :
A = P (1 + _{100}R ) ² × (1 +
1
5R
100)

When rates are different for different years,say R1%, R2%...Rn% for 1st

year, 2nd year…..nth year respectively, then
A = P (1 + R1
100) (1 +
R_{2}
100) ……. (1 +
R_{n}
100)

*If Diff. between SI & CI for 2 years is Rs. x, then *
Principal = (C.I ~ S.I) (100_{R} )

### ²

*= x (*100

_{R})

### ²

(C.I ~ S.I) = P ( R100)

### ²

Diff. between SI & CI for 3 years : (C.I ~ S.I) = P ( R

100)

### ²

× (**Population : **

Let the population of the town be P now and suppose it increases at the rate of R% per annum,then:

* Population after n years = P [1 + * R

100 ]

n_{ (After n years population }

increases, thus (1 + R

100) is used and if population decreases, (1 − R 100) is

used)

* Population n years ago = * 𝑃

[ 1 + 𝑅 100 ]𝑛

**SOLVED EXAMPLES: **

**1) Find the Simple Interest on a sum of Rs.2000 at 8% per annum for 3 **
**years? **
(a) Rs.300 (b) Rs.480
(c) Rs.500 (d) Rs.400
**Ans: (b) Rs.480 **
** Formula: ** S.I = (P × R × T)
100 ** **

Given that, Principal P = Rs.2000, Rate R = 8% and Time T = 3 years

Simple Interest, S.I = (P × R × T)

100

S.I = (2000 × 8 × 3)

100

**2) Find the Simple Interest on Rs.4000 for 3 years at the rate of 10% per **
**annum. Also, find the amount. **

(a) Rs.1200, Rs.5200
(b) Rs.1600, Rs.4000
(c) Rs.1100, Rs.4400
(d) Rs.1500, Rs.6500
**Ans: (a) Rs.1200, Rs.5200 **
** Formula: ** S.I = (P × R × T)
100 ** **
A = P + S.I
Given that, Principal P = Rs.4000,
Rate R = 10%
and Time T = 3 years

Simple Interest, S.I = (P × R × T)

100 S.I = (4000 × 10 × 3) 100 S.I = Rs.1200 Amount, A = P + S.I A = 4000 + 1200 A = Rs.5200

**3) Simple interest on a sum at 3 **𝟏

𝟐 **% per annum in 4 years is Rs.70. Find **
**the sum. **

**Ans: (b) Rs.500 **

** Formula: P = ** S.I × 100

R × T ** **

Given that, Simple Interest S.I = Rs.70,
Time T = 4 years
** and Rate R = 3 **1
2 % =
7
2 %
Principal, P = S.I × 100
R × T ** **
P = 70 × 1005
2 × 4
** **
P = 7000
14
P = Rs.500

**4) Pramod took Rs.1100 from Ajay at 8% interest per year. How much **
**will he return to Ajay after 6 months? **

(a) Rs.1120 (b) Rs.1088
(c) Rs.1050 (d) Rs.1144
** Ans: (d) Rs.1144 **
** Formula: ** S.I = (P × R × T)
100 ** **
** A = P + S.I **
Given that, Principal P = Rs.1100,
Rate R = 8%

** and Time T = 6 months = **6

Simple Interest, S.I = (P × R × T)
100
S.I = 1100 × 8 ×
1
2
100
S.I = Rs.44
** Amount, A = P + S.I **
A = Rs.1100 + Rs.44
A = Rs.1144

**5) At what rate per cent, simple interest will a certain sum of money **
**double itself in 20 years? **

(a) 30% (b) 20%
(c) 5% (d) 15%
**Ans: (c) 5% **
** Formula: S.I = A – P **
R = S.I × 100
P × T ** **

* Let the Principal P = Rs.x, *
* Amount A = Rs.2x *
** and Time T = 20 years **
S.I = A – P

* ⇒ S.I = 2x – x *
* ⇒ S.I = Rs.x *
R = S.I × 100

R = 𝑥 × 100

𝑥 × 20 ** **

R = 5%

**7) In what time, will the simple interest on the sum of Rs.2600 will be **
**Rs.288 at 8% per annum? **
(a) 1 5
13 years

### (b) 5 years (c) 3 years (d) 2 1 2 years

**Ans: (a) 1**5 13 years

**Formula: T =**S.I × 100 P × R

Given that, Principal P = Rs.2600,
Rate R = 8%
and Simple Interest S.I = Rs.288
T = S.I × 100
P × R ** **
T = 288 × 100
2600 × 8 ** **
T = 18
13 ** years **
T = 1 5
13 years.

**8) Kamal lent Rs.600 to Meena for 2 years and Rs.150 to Anil for 4 years **
**and received altogether from both Rs.90 as simple interest. Find the **
**rate of interest. **

**Ans: (a) 5% **

Given that, Principal, P1 = Rs.600

Time, T1 = 2 years

Principal, P2 = Rs.150

Time, T2 = 4 years

And Total interest,S.I = Rs.90
P1 x R x T1
100 +
P2 x R x T2
100 = 90
600 x R x 2
100 +
150 x R x 4
100 = 90
1200 x R
100 +
600 x R
100 = 90
12 R + 6 R = 90
18 R = 90
R = 90
18
** ⇒ Rate of interest, R = 5%**

**9) What will be the Compound Interest for the sum of Rs.8000 after 3 **
**years at the rate of 5% p.a? **

(a) Rs.1320 (b) Rs.1500
(c) Rs.1261 (d) Rs.1100
** Ans: (c) Rs. 1261 **
** Formula: A = P (1 + ** R
100)
n** _{ }**
C.I = A – P

Rate R = 5% and Time n = 3 years Amount, A = P (1 + R 100) n = 8000 (1 + 5 100 ) 3 = 8000 ( 105 100 ) 3 = 8000 (21 20 ) 3 = 8000 x 21 20 x 21 20 x 21 20 A = 9261

Compound Interest, C.I = A – P

= 9261 – 8000 = Rs.1261

**10) ** **A certain sum amounts to Rs.5832 in 2 years at 8% compound **
**interest. Find the sum. **

(a) Rs.6000 (b) Rs.5000
(c) Rs.5500 (d) Rs.4500
** Ans: (b) Rs. 5000 **
** Formula: A = P (1 + ** R
100)
n_{ }

Given that, Amount A = Rs.5832, Rate R = 8%

and Time n = 2 years Amount, A = P (1 + R

5832 = P

### (1 +

8 100### )

2 5832 = P### (

100 + 8 100### )

2 5832 = P### (

108 100### )

2 5832 = P### (

27 25### )

2 5832 = P x 27 25 x 27 25 P = 5832 x 25 27 x 25 27 P = Rs.5000**11) ** **At what rate percent will a sum of Rs.1000 amount to Rs.1331 in **
**3 years at compound interest? **

(a) 14% (b) 7%
(c) 6% (d) 10%
** Ans: (d) Rs. 10% **
** Formula: A = P (1 + ** R
100)
n_{ }

(11
10)
3_{ = (1 + } R
100)
3_{ }
⇒ 1 + R
100 =
11
10

### ⇒ R 100 = 11 10

### –

1### ⇒ R 100 = 11 − 10 10 ⇒ R 100 = 1 10 ⇒ R = 1 10 x 100 ⇒ Rate of interest, R = 10%

**12) ** **Abhay lent Rs.5000 to his friend for 3 years at the rate of 10% **
**per annum compound interest. What amount does Abhay get after 3 **
**years? **
(a) Rs.6000 (b) Rs.6655
(c) Rs.5665 (d) Rs.5160
** Ans: (b) Rs. 6655 **
** Formula: A = P (1 + ** R
100)
n_{ }

= 5000 (22 20 ) 3 = 5000 x 22 20 x 22 20 x 22 20 A = 6655

**13) ** **A sum of money deposited at 2% per annum compounded **
**annually becomes Rs.10404 at the end of 2 years. Find the sum **
**deposited. **
(a) Rs.8000 (b) Rs.10000
(c) Rs.12000 (d) Rs.9000
** Ans: (b) Rs. 10000 **
** Formula: A = P (1 + ** R
100)
n_{ }

Given that, Amount A = Rs.10404, Rate R = 2%

**14) ** **In how many years, will Rs.6,000 amount to Rs.6,615 **
**compounded annually at the rate of 5% per annum? **

(a) 4 years

### (b) 8 years

(c) 2 years (d) 10 years

**Ans: (c) 2** years

** Formula: A = P (1 + ** R

100)
n_{ }

**15) ** **The difference between the simple interest and the compound **
**interest(compounded annually) at the rate of 12% per annum for two **
**years is Rs.72. What will be the sum? **

(a) Rs.6000 (b) Rs.5400 (c) Rs.6250 (d) Rs.5000

** Ans: (d) Rs. 5000 **

** Formula: (C.I ~ S.I) = P **

### (

𝑅100

### )

2_{ }