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SIMPLE AND COMPOUND INTEREST
Interest is the additional money paid for the
usage of a certain amount.
★ The amount borrowed is called the principal.
★ The sum of interest and principal is called
the amount.
Simple Interest
If the interest is calculated on same amount
of money it 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 time and S.I. the simple interest, then
PTR
Simple Interest = ⎯
100
TR
Amount = P 1+ ⎯
100
Note: Simple interest is always calculated on
principal. Therefore simple interest is
equal for every period.
e.g: 1. What would be the simple interest
★
[
]
interest, P is the principal, R is the rate, and T
is the time, then
R
T
A = P 1+ ⎯
100
R
T
C.I = P 1+ ⎯ - P
100
e.g: What is the compound interest accrued on
an amount of Rs.8000, at the rate of 6%
p.a. at the end of 2 years?
(A) Rs.2545 (B) Rs.2,257.20 (C) Rs.2986
(D) Rs.2775.40 (E) None of these
T
R
Solution: C.I. = P 1+ ⎯ - P
100
2
6
C.I. = 8000 1+ ⎯ - 8000
100
⇒ Rs.988.80
Shortcut: Amount =106% of 106% 8000
= 8988.80
∴ C.I. = 8988.80-8000 = Rs.988.80
Note: 1. If the interest is paid half yearly, time
[
]
[
]
[
]
[
]
2
24000×49
10000
= Rs.117.60
2. On what sum does
the
difference
between Simple
and Compound
Interest for 3 years
at 5% rate will be Rs.244?
(300+R)P×R2
Sol: Difference = ⎯ ⎯ ⎯
1003
(300+5)P×25
⇒ 244 = ⎯ ⎯ ⎯ ⇒ P = Rs.32000
1000000
⇒ ⎯⎯
Some other Models of Questions:
1. A sum of money will become Rs. 8060 in 4
years at 6% per annum simple interest. Find
the sum.
TR
Sol: Amount = P 1+ ⎯
100
[
]
What is the rate of interest per annum?
[
]
obtained on an a amount of Rs. 6850 at
the rate of 6 p.c.p.a. after 3 years?
(A) Rs.2423 (B) Rs.1233 (C) Rs.1633
(D) Rs.1525 (E) None of these
Sol: Here P = Rs. 6850, T= 3 years and R = 6%
PTR
Simple Interest = ⎯
100
6850×3×6
= ⎯⎯ = Rs.1233
100
Hence answer is (B)
2. How long will it take for Rs.1250 to become
Rs. 1600 at 7% per annum simple interest?
(A) 5 years
(B) 3 years
(C) 4 years
(D) 6 years
(E) None of these
PTR
Sol: Simple Interest = ⎯
100
S.I×100
⇒T= ⎯⎯
P×R
(1600-1250)×100
⇒T= ⎯⎯⎯⎯ = 4 years
1250×7
Hence Answer is (C)
3. What would be the amount on Rs.8250 for
4 years at 15% per annum simple interest?
(A) Rs.13200 (B) Rs.12300 (C) Rs.10450
(D) Rs.11200 (E) None of these
TR
Sol: Amount = P 1+ ⎯
100
4×15
Amount = 8250 1+ ⎯ = Rs.13200
100
Shortcut: for one year, rate of interest is 15%
and for 4 years it is 15×4 = 60% The
Amount will become 160%
If 100% Money = 8250,
160
160% money = ⎯ ×8250 = Rs.13200
100
Compound Interest:
Interest which is calculated not only on the
initial principal but also the accumulated interest of prior periods.
If A is the amount, C.I. is the compound
4×6
100
8060×100
⇒ P = ⎯ ⎯ ⎯ = Rs.6500
124
Shortcut: For one year, rate of interis doubled and the rate is
est is 6% and for 4 years
halved.
it is 4×6%=24%
2. If the interest is paid quar- G.S. GIRIDHAR Then the amount will become 124%
terly, time becomes 4 times and the
If 124% money is Rs. 8060, 100% money
rate becomes onefourth
100
will be ⎯ ⎯ ⎯ ×8060 = Rs.6500
e.g: What is the interest accrued on Rs.12000
124
for one and half year at 4% p.a. com2. Find the simple interest on Rs.17500 at 7%
pounded half yearly?
per annum from August 5th to October 17th
in the same year.
1 × 2 = 3,
Sol: P= Rs.12000, T= 1 ⎯
2
Sol: Time from August 5th to October 17th
R=4
⎯ = 2%
= 26 days of August + 30 days of
2
T
September and 17 days of October
R
C.I. = P 1+ ⎯ - P
100
73
1
= 73 days = ⎯ year = ⎯ years
3
365
5
2
⇒ 12000 1+ ⎯ -12000
1
100
17500×7× ⎯
5
⇒ 12734.496 -12000 = Rs.734.496
∴ S.I. = ⎯ ⎯ ⎯ ⎯ = Rs.245
100
Difference between Simple and Compound
3. A sum was put at simple interest at a certain
Interest
rate for 2 years. Had it been put at 3% highDifference between Simple Interest and
er rate, it would have fetched Rs.72 more.
Compound Interest can be calculated by using
What is that sum?
formulae.
Sol: Interest for 2 years is Rs.72. For one year
There is no difference between Simple and
it is Rs.36
Compound Interest for one year.
3% interest money is Rs.72, then 100% money
For 2 years
100
P×R2
= ⎯ × 36 = Rs.1200
Difference = ⎯
3
1002
∴ Sum is Rs.1200
For 3 years
4. A certain sum of money invested at com(300+R)P×R2
Difference = ⎯ ⎯ ⎯
pound interest doubles in 3 years. In how
3
100
many years will it become 6 times itself?
e.g: 1. What is the difference between Simple
Sol: Let the money be Rs. x
and Compound Interest for two years
It becomes Rs. 2x in 3 years
on Rs.24000 at 7% rate?
As this is compound interest, 2x will be the
Sol:
principal for next period.
P×R2
Difference = ⎯
Therefore, 2x will become 4x in next 3 years
1002
EXPLANATIONS
1. Simple Interest = Amount - Principal
= 5952 - 4800 = Rs.1152
1152 × 100
Time = ⎯⎯⎯ = 4 years
4800 × 6
2. Total Money lent to Varun for 4 years
= 4× Rs.1500 = Rs.6000
Total money lent to Sandeep for 2 years
= 2× Rs.4500 = Rs.9000
total money lent = 6000+ 9000 = Rs.15000
Interest received = Rs. 750
750
Interest % = ⎯⎯ × 100 = 5%
15000
3. Total interest received for 6 years =
Rs.5000 + 400 = Rs.5400
5400
interest for one year = ⎯⎯ = Rs.900
6
900
interest % = ⎯⎯ × 100 = 18% pa
5000
T
R
4. C.I. = P 1+ ⎯ - P
100
3
7
C.I. = 18000 1+ ⎯ - 18000
100
⇒ Rs.4050.7740
5. Rs.980-Rs.944 = 36
25% of interest = Rs.36
36×100
100% = ⎯ ⎯ = Rs.144
25
Hence the interest for three years = Rs.144.
Therefore Principal = 944-144= Rs.800
144×100
interest% = ⎯ ⎯ = 6%
800×3
6. Let the population of the town in 2005 be 'x'
∴104% of 104% of x = 59488
[
]
[
]
⇒ 8060 = P 1+ ⎯
NUMERICAL ABILITY
[
]
[
]
[
]
[
]
100
100
x = 59488 × ⎯ × ⎯ = 55000
104
104
7. Amount after 5years = 9100
Amount after 8 years = 10660
Difference = 1560, which is interest for 3years
5
Interest for 5 years = ⎯
×1560 = 2600
3
Principal = 9100 - 2600 = 6500
S.I.×100
2600×100
R = ⎯ ⎯ = ⎯ ⎯ = 8%
P×T
6500 × 5
P×R2
9. Difference = ⎯
1002
24000×4×4
⇒ ⎯ ⎯ = Rs.38.40.
100×100
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hence Rs. x will become 4x
i.e. 4 times in 3 + 3 = 6 years
5. A man deposits Rs. 12600 in a bank at 5%
annual interest. After 8 months he withdraws Rs.5400 together with interest and
after 4 months the remaining money. How
much does he get as interest at the end of
the year?
Sol: S.I. of Rs.12600 for 8 months
8
12600 × ⎯
×5
12
= ⎯ ⎯ ⎯ = Rs.420
100
He withdrew Rs.5400 together with interest, the remaining amount
= 12600 - 5400 = Rs.7200
S.I. on Rs.7200 at the rate of 5% for 4 months
4 = ⎯
1 years
= ⎯
12
3
1
7200 × ⎯
×5
3
= ⎯ ⎯ ⎯ = Rs.120
100
Total interest = 420 + 120 = Rs.540
EXERCISE
1. In what time will Rs.4800 amount to Rs.5952
at 6% per annum?
A) 4 years
B) 6 years C) 2 years
D) 3 years E) None of these
2. Varun lent Rs.1500 to Sandeep for 4 years
and Rs.4500 to Ravi for 2 years. If he
receives Rs.750 as simple interest altogether, find the rate of interest.
A) 4% B) 2% C) 5% D) 3% E) None
3. Avanthi borrowed Rs. 5000 from Keerthi at
simple interest. If Keerthi got Rs. 400 more
than her capital after 6 years, what is the rate
of interest per annum?
A) 12% B) 15% C) 9% D) 6% E) 18%
4. What is the compound interest accrued on
an amount of Rs.18000, at the rate of 7
p.c.p.a at the end of 3 years?
A) Rs. 4125.5650 B) Rs. 4050.7740
C) Rs. 3570.2560 D) Rs.s 4355.2750
E) None of these
5. A sum of money amounts to Rs. 944 in 3
years at a simple interest. If the rate of interest is raised by 25%, the sum amounts to
980 during the same period. Find the sum
and the rate of interest.
A) 4%
B) 2%
C) 5%
D) 3%
E) None of these
6. The population of a town increases by 4%
every year. If its population in 2007 was
59488, what was its population in 2005?
A) 56000
B) 54000
C) 55000
D) 50000
E) None of these
7. A sum of money will become Rs. 9100 in 5
years and 10660 in 8 years at a certain
rate of simple interest. Find the rate of
interest.
A) 4%
B) 3%
C) 5%
D) 8%
E) None of these
8. A sum of Rs. 15475 will become double in 4
years at a certain rate of compound interest.
In what time will it become eight times itself?
A) 12 years B) 8 years C) 10 years
D) 6 years
E) None of these
9. What is the difference between simple interest and compound interest for two years at
4% on Rs. 24000?
A) Rs. 33.50
B) Rs. 42
C) Rs. 38.40
D) Rs. 38.50
E) None of these
ANSWERS:
1) A 2) C 3) E 4) B 5) E
6) C 7) D 8) A 9) C .