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SBI PROBATIONARY OFFICERS
QUANTITATIVE APTITUDE
SIMPLE AND COMPOUND INTEREST
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Simple Interest:
If the interest is calculated on original Principal for a certain period is called the Simple Interest (S.I.).
Simple Interest will be the same for all the years. If P is the principal, R is the rate of interest, T is the time
and S.I. is the simple interest, then
(
PTR
100
Simple Interest =
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)
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TR
Amount = P 1 + 
100

★
Interest is the money that paid for the use of a certain amount.
★
The amount borrowed is called the Principal.
★
The sum of interest and principal is called the Amount.
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Compound Interest:
The compound interest is the interest which is calculated even on the interest. Thus the amount at the
end of period becomes the principal for the next period.
★
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If A is the amount, C.I. is the compound interest, P is the principal, R is the rate, and T is the time, then
R
A = P 1 + 
100
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T
R
C.I = P 1 + 
100
)
.
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T
−
P
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Note: If the Interest is paid half yearly, time is doubled and the rate is halved.
★
If the Interest is paid quarterly, time becomes 4 times and the rate becomes one fourth.
Difference between Simple and Compound Interest
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Difference between Simple Interest and Compound Interest can be calculated by the following
formulae.
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★
There is no difference for one year.
★
For 2 years
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Difference =
★
P × R2

1002
For 3 years
Difference =
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R-19-5-15
(300 + R) P × R2

100 3
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EXERCISE
1.
2.
3.
4.
1
What principal will amount to Rs.8550 at 4% per annum simple interest in 3  years?
2
1) Rs.6800
2) Rs.7500
4) Rs.7300
5) None of these
1) Rs.20837.25
2) Rs.21525
4) Rs.19300.50
5) None of these
1) Rs.600
2) Rs.625
4) Rs.675
5) None of these
8.
9.
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3) Rs.700
What will be the amount on Rs.25000 in 2 years at compound interest, if the rates for the successive
years be 4% and 5% per year?
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2) Rs.26,725
3) Rs.27,300
5) None of these
A sum of Rs.1400 becomes Rs.1652 in three years at certain rate of simple interest. What will be the
amount if the rate of interest is increased by 3%?
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7.
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b
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3) Rs.2837.25
A sum of money invested at compound interest will become Rs.650 at the end of first year and 676 at
the end of second year. What is the sum?
4) Rs.27,675
6.
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What is the compound interest accrued on an amount of Rs.18000, at the rate of 5%, at the end of 3
years?
1) Rs.26,800
5.
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3) Rs.8100
1) Rs.378
2) Rs.1748
4) Rs.1778
5) None of these
3) Rs.1586
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a
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A sum was invested at simple interest at a certain rate for two years. It would have fetched Rs.240 more
had it been invested at 3% higher rate. What was the sum?
1) Rs.8,500
2) Rs.4,500
4) Rs.9,000
5) None of these
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3) Rs.5,600
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Population of a town in 2011 was 85000. What will be the population in 2014, if it increases annually
at 10%?
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1) 113135
2) 11400
4) 11600
5) None of these
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3) 11500
The rate of simple interest on a certain amount of money is 6% p.a. for the first two years, 9% p.a. for
next five years and 13% p.a. for the period beyond seven years. If the total interest on a sum at the end
of ten years is Rs.9120, what is the sum?
1) Rs.9500
2) Rs.10500
4) Rs.11750
5) None of these
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3) Rs.12500
1
What is the compound interest on Rs.25000 for 1  year at 8% per annum, interest being calculated
2
half yearly?
1) Rs.3225
2) Rs.3050.50
4) Rs.2995.50
5) None of these
3) Rs.3121.60
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10.
11.
12.
13.
A certain sum of money lent out at a certain rate of simple interest per annum doubles itself in 8 years.
In how many years will it treble itself?
1) 12
2) 18
4) 16
5) None
1) 9 yrs
2) 6 yrs
4) Can't be determined
5) None
3) 12 yrs
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A certain sum of money becomes Rs.1250 in a span of 5 years and further to Rs.1700 in the span of 8
years at the same rate of simple interest. What would be the amount at the end of 12 years?
1) Rs.2325
2) Rs.2500
4) Rs.2990
5) None of these
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3) Rs.2650
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What is the difference between simple and compound interest for three years on Rs.16000 at 8% p.a?
2) Rs.122
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4) Can't be determined
15.
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A sum of money will become double in 3 years at compound interest. In what time will it become four
times itself?
1) Rs.348
14.
3) 24
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3) Rs.496
5) None
A sum of money amounts to Rs.1488 in 3 years at a simple interest. If the rate of interest is raised by
25%, the sum amounts to 1560 during the same period. Find the sum.
1) Rs.1350
2) Rs.1500
4) Rs.1250
5) None of these
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h
A sum of Rs.7200 is lent out in two parts in such a way that the interest on one part at 8% p.a for 3
years is same as on the other part at 5% p.a. for 6 years. Find the first part.
1) Rs.3200
2) Rs.3600
3) Rs.3300
4) Rs.1800
5) None of these
KEY
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1-2; 2-3; 3-2; 4-3; 5-4; 6-5; 7-1; 8-1; 9-3; 10-4; 11-2; 12-5; 13-5; 14-3; 15-5.
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EXPLANATIONS
1.
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3) Rs.1200
)
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(
Amount = P 1 +
TR
100

7 ×4
2 × 100
⇒ P 1 +  = 8550
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8550 × 2 × 100
228
⇒ P =  = Rs.7500
Shortcut:
1
1
For one year, rate of interest is 4% and for 3  years it is 4 × 3  = 14%
2
2
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The amount will become 114%.
If 114% money = 8550, then 100% money
100
=  × 8550 = Rs.7500
114
2.
(
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)
R T
C.I = P 1 +  - P
100
5 3
C.I = 18000 1 +  − 18000
100
(
[
)
]
105
105
105
⇒ 18000 ×  ×  ×  − 18000
100
100
100
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t
a
r
= 2837.25
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Shortcut:
Amount = 105% of 105% of 105% of 18000
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= 20837.25
∴ C.I = 20837.25 − 18000 = Rs.2837.25
3.
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w ( )
Interest on Rs.650 is 676 − 650 = Rs.26
26
∴ Rate of interest =  × 100 = 4%
650
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R T
Amount = P 1 + 
100
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)
650 × 100
4 1
650 = P 1 +  ⇒ P = 
100
104
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= Rs.625
4.
(
4
Amount is 25000 1 + 
100
)(
5
1+ 
100
)
25000 × 104 × 105
⇒ A =  = Rs.27300
100 × 100
5.
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p
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100 × SI
100 × 252
R =  ⇒ R =  = 6%
P× T
1400 × 3
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Now the rate of interest is 6 + 3 = 9%
TR
∴ New amount is P 1 + 
100
3× 9
= 1400 1 +  = Rs.1778
100
w
Shortcut:
If the rate of interest is increase by 3% then the amount will also increase by that much
1400 × 3 × 3
New interest is  = Rs.126
100
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∴ New amount is 1652 + 126 = Rs.1778
6.
It fetches Rs. 240 more in 2 years.
It fetches Rs.120 more in one year.
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that means 3% = Rs.120
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100% (sum) is  × 120 = Rs.4000
3
7.
Population after 3 years (2014 - 2011) is
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110% of 110% of 110% of 85000 = 113135
8.
Let the principal be Rs.x
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x× 2× 6
x× 5× 9
x × 3 × 13
 +  +  = 9120
100
100
100
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x
⇒  (12 + 45 + 39) = 9120
100
⇒ x = Rs.9500
9.
a
n
1
As interest is calculated half yearly, 1 − will be 3 half years and the rate percent will be 4% per half
2
year.
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)
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w
now, R = 4% and T = 3
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4 3
C.I. = 25000 1 +  − 25000
100
10.
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= Rs. 3121.60
Let the principal be Rs.P and the amount will be Rs.2 P
100 × (2P − P)
Rate of interest per annum is  = 12.5%
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P× 8
100 × (3P − P)
Required time is  = 16 years
P × 12.5
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Shortcut:
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Amount doubles in 8 years means to get 100% interest it takes 8 years
★ To become treble means to get 200% interest it takes 8 + 8 = 16 years
11.
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Let the money be Rs.100
It becomes Rs.200 in 3 years
★ Again Rs.200 will become Rs.400 in another 3 years (... Compound interest)
∴ amount will become four times in 3 + 3 = 6 years
12.
w
Interest for 3 years (8 − 5 years) = 1700 − 1250 = Rs.450
5
Interest for 5 years =  × 450 = Rs.750
3
Principal = 1250 − 750 = Rs.500
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12
Interest for 12 years =  × 450 = Rs.1800
3
∴ Amount after 12 years = 500 + 1800
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= Rs.2300
13.
(300 + R)P × R2
Difference for 3 years is 
1003
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a
308 × 16000 × 100
⇒  = Rs.492.80
1000000
14.
h
b
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Rs.1560 − Rs.1488 = 72.
t
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25% of interest = Rs.72
100
∴ 100% interest =  × 72 = Rs.288
25
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The interest for three years = Rs.288.
Therefore Principal = 1488 − 288
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= Rs.1200
15.
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w
Let the first part be Rs.x, then the second part will be (7200 − x)
x× 3× 8
(7200 − x) × 5 × 6
∴  = 
100
100
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⇒ x = Rs.4000
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Writer: Dr. G.S. Giridhar
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