www.ssccglpinnacle.com
Gurudwara Road Model Town, Hisar 9729327755 www.ssccglpinnacle.com
SSC CGL Tier 1 and Tier 2 Program
------------------------------------------------------------------------------------------------------------------Section : Math
Chapter : Compound Interest
Days 42 -45
---------------------------------------------------------------------------------------------------------------------------------------------Compound Interest
Significance:


0- 1 question can come in tier 1 and 1-2 questions in tier 2.
1 or 2 questions can create a lot of difference in a high competitive en
Key concepts / Tricks







For one year or one term simple interest and compound interest are same.
In simple interest you divide the simple interest by number of years to calculate one year interest but
in compound interest not applicable.
It is preferable to solve questions without formula or minimum formula as per my view. Also see my
video lecture once it is uploaded. Important tips are given in video.
Compound Interest: Interest on amount ( principal + Interest) ; Symbol we will use CI.
Let us say one person borrow money Rs 100 for 3 years at the rate of 10% annually. What amount
should he have to return after 3 years?
Let us learn approximate technique which is given below
100
10%
110
10% =11
10%=12.1
121
133.10
Compound Interest will be 133.10-100 =33.1

You can also write the above stuff like this ; Amount =

Or you can express like this Amount = Principal (1 +


×
×
×
×
×
) = 100 1 +
= 133.10 ; CI =133.10-100=33.10
=100×
×
×
=133.10;
CI=33.10
So all above three concepts have the same result; but you want to solve questions without formula then develop
mastery on approximation trick.
If rate of interest is different for different year let us say 10% for 1st year, 20% for 2nd year and 30% for 3rd year
then amount will be equal to

100
10%
110
20% =22
132
30%=39.6
171.60
Pinnacle SSC CGL Coaching, Gurudwara Road, Model Town, Hisar 9729327755 www.ssccglpinnacle.com
Page 1
www.ssccglpinnacle.com

i.e. 100 ×
×
×
=171.60 ; you will find easy to calculate through approximation.
Let us further understand the concepts /tricks through Project 400 Questions.
Q1. Compound Interest compounded annually on a certain sum of money for 2 years at 4% per annum is Rs
102. The simple interest on the same sum for the same rate and for the same period will be
(a) Rs 99
(b) 101
(c) RS 100
(d) Rs 98
Solution:( c) Through approximation trick (without formula)
Let principal Rs 100 ; SI for 2 years @ 4% will be =Rs 8
Now for compound Interest
4%
100
4% =4.16
104
108.16
CI = 108.16 -100=8.16 ; We can use successive %age technique here
ℎ
4%
If 8.16 CI then SI is =8
If CI 102 then Si will be =
4+4+
.
+
+
; here
=8.16
× 102 =100
Remember it
2nd Method through trick
) ; 102 = SI (1 +
For 2 years relationship for CI and SI is ; CI =SI (1 +
) ; After solving we get SI =100
Q2. If the amount is 2.25 times of the sum after 2 years at compounded interest (compounded annually), the
rate of interest per annum is:
(a) 25% b) 30% c) 45% d) 50%
Solution ( d): CI = SI (1 +
=1+
) ; Let us take principal 100; 225 =100 1 +
;
=
= 1+
;
; r =50
Q3. The compound interest on Rs 10,000 in 2 years at 4% per annum, the interest being compounded half
yearly, is:
a) Rs 636.80
b) RS 824.32
Solution (b) 100
c) Rs 912.86
2%
d) 828.82
2%=2.04
102
2%= 2.0808
104.04
106.1208
2% =2.122416
108.243216
CI = 108.243216 -100= 8.243216; on 10000 CI will be =824.3216
Or alternatively you can solve ; CI = P (1 +
) −1
Pinnacle SSC CGL Coaching, Gurudwara Road, Model Town, Hisar 9729327755 www.ssccglpinnacle.com
Page 2
www.ssccglpinnacle.com
×
CI = 10000×
×
×
=824.32
Q4. If the difference between the compound interest, compounded every six months, and the simple interest
on a certain sum of money at the rate of 12% per annum for one year is Rs 36, the sum is:
a) Rs 10,000 b) Rs 12000 c) Rs 15000 d) Rs 9000
Solution (a) How to solve questions related to difference (D =CI-SI)?
1st approximation technique
Here we will take 2 terms, 6% each i.e. 12% yearly but compounded half yearly ( Rs 6 in 6 months on Rs 100)
SI = 6*2 =12 on Rs 100
CI:
6%
6% =6.36
100
106
112.36
CI= 112.36 -100 =12.36
; also you can calculate through % trick
Difference (D) = 12.36-12 =.36
If .36 is the difference then Principal is 100
×
If 36 is the difference then principal is =
= 10,000
+
+
=
+ +.
=
.
.
×
2nd Math through formula : for 2 years D =
; 36 =
× ×
;
= 10000
Q5. In how many years will Rs 2000 amount to Rs 2420 at 10% per annum compound interest?
(a) 3 b) 5/2 c) 2 d) 3/2
Solution (c)
Amount = P 1 +
; 2420 = 2000 1 +
;
=
=
; we get t=2 years
Q6. A sum of money invested at compound interest amount to Rs 650 at the end of first year and Rs 676 at the
end of second year. The sum of money is:
a) Rs 600 b) RS 540 c) Rs 625 d) Rs 560
Solution (c)
650 ; Rate =
Interest for one year simple and compound is equal. In 2nd year, Interest =676-650 = Rs 26 on Rs
×
=
= 4%. If 100 is principal then amount at the end of 1 year =104.
×
×
×
If amount is 650 then Principal will be =
× 650 = 625
Or alternatively you can say that if 676 is amount then principal =650
×
If 650 is amount then principal =
= 625
Q7. A sum borrowed under compound interest doubles itself in 10 years. When will it become fourfold of itself
at the same rate of interest?
a) 15 years
b) 20 years
c) 24 years
d) 40 years
10 years
Pinnacle SSC CGL Coaching, Gurudwara Road, Model Town, Hisar 9729327755 www.ssccglpinnacle.com
Page 3
www.ssccglpinnacle.com
Solution (b)
100
200
20 yrs i.e. next 10 years
200
400
Q8. If the difference between the compound interest and simple interest on a sum at 5% rate of interest per
annum for three years is Rs 36.60, then the sum is
a) Rs 8000
b) Rs 8400
c) Rs 4400
d) Rs 4800
Solution (d) For 3 years you can solve by using this trick D =
36.60 =
×
(
×
)
×
×
×(
(
)
)
= 4800
Alternatively you can solve through approximation without formula
SI = 5× 3 = 15
Used successive % age directly
100
For CI ; 5 +5 +.25 =10.25 ; 10.25 +5 +
If D is .7625 then sum is =100
×
If D is 36.60 then sum is =
.
.
.
×
= 15.7625 ; D =.7625
= 4800
Q9. A sum becomes Rs 4500 after two years and Rs 6750 after four years at compound interest. The sum is
a) 4000
b) Rs 2500
Solution (c)
c) Rs 3000
×(
)
×(
)
= (1 +
d) Rs 3050
) =
=
;
× (1 +
) = 4500 ;
× = 4500 ;
= 3000
Or you can think like this
=
4500 becomes 6750 in 2 years;
2
= 4500 ℎ ℎ
2
;
= 4500 × = 3000
Q10. A loan of Rs 12300 at 5% per annum compound interest is to be repaid in two equal
annual installments at the end of every year. Find the amount of each installment.
a) RS 6651 b) Rs 6615 c) Rs 6516 d) RS 6156
Solution (b)
(1 +
let us take
) = 12300;
as installment; equation is
×
+
×
×
×
=12300
= 6615
.
.
1
105 ℎ ℎ
100
Pinnacle SSC CGL Coaching, Gurudwara Road, Model Town, Hisar 9729327755 www.ssccglpinnacle.com
5%.
Page 4