Introduction:
If the interest at the end of a year or fixed period is
added to the sum lent, and the amount thus obtained becomes the principal for
the next period, then sum of the money is said to be lent at compound interest.
If P is the principal, T is the number of years and R
is the rate of interest per annum.
Amount= P [ 1 +
R
100
]T
Note
1 : When the interest is compounded half
yearly
Amount= P[1 +
R/2
100
]2T = p[1+
R
200
]2T
Note
2: When the interest is compounded quarterly
Amount= P[1 +
R/4
100
]4T = p[1+
R
400
]4T
Compound interest is obtained by when principal is
subtracted from the amount.
Solved Problems on Compound Interest
1.
Find the
compound interest on Rs 80000 for 3
years at 5% per annum rate of interest?
a)Rs 12000 b)Rs 12610 c)Rs 14800 c)Rs 15300
Answer:B
Explanation:
Here, the given principal is Rs 80000. The time period is 3 years , and the rate of
interest is 5%.
A =P [ 1 +
R
100
]T => A= 80000 [1+
5
100
]3
ð A
= 80000 x $\frac{21}{20} $x $\frac{21}{20} $x $\frac{21}{20}$
ð A=
Rs 92610
Compound Interest = Amount – Principal
=(92610 – 80000) = Rs 12610
=(92610 – 80000) = Rs 12610
2.
Find the
compound interest on Rs 24000 at 10% per
annum for 2 years 6 months
a)
Rs 6492 b)Rs 6200 c)Rs 6000 d)Rs 5825
Answer :A
Explanation:
Principal = Rs 24000 Rate of interest =
10% p.a
Time Period = 2 ½ years
For 2 years , the rate of interest is 10% and for next
6 months rate of interest will be 10%/2= 5%
Amount => A = Rs 24000 ( 1 +
10
100
)2 ( 1
+
5
100
)
A= 24000 x
110
100
x
110
100
x
105
100
A
= 24000 x
11
10
x
11
10
x
21
20
=30492
Compound interest
= Amount – Principal
= (Rs 30492 – Rs 24000) = Rs 6492
= (Rs 30492 – Rs 24000) = Rs 6492
3.
Find the Compound
interest on Rs 5000 in 2 years, the rate of interest being 5% for the first
year and 10% for the second year ?
a)Rs 775 b)
Rs 3875 c)Rs 1650 d)Rs 2150
Answer: A
Explanation:
Given Principal = Rs 5000 T= 2 years and Rate of interest for 1st
year is 5% and 2nd year is 10% => R1= 5% and R2= 10%
A=
[1+
R1
100
][1+
R2
100
]
A = 5000 x [ 1+
5
100
[1+
10
100
]
=>A=5000 x
=> A= Rs 5775
21
20
x
11
10
==> A= Rs 5775
∴ Compound interest= (A – P) => (5775 – 5000) = Rs 775
4.
At what rate
percent per annum compound interest will Rs 12500 amount to Rs 13520 in 2 years
?
a)13% b)10% c)8% d)4%
Answer: D
Explanation:
Amount A= Rs 13520 Principal = Rs 12500 Rate of Interest= R and Time period T =
2 years
A =P [ 1 +
R
100
]T => 13520 = 12500 [ 1 +
R
100
]2
=>
13520
12500
13 = [ 1 +
R
100
]2
=>
676
675
= [
1 +
R
100
]2
=> (
26
25
)2=
[ 1 +
R
100
]2
=> [ 1 +
R
100
] =
26
25
=>
R
100
=
1
25
Therefore,
the rate of interest is 4%.
5.
What sum will
amount to Rs 30000 in 3 years at 25% p.a compound interest?
a)
Rs 15000 b) Rs 15360 c)Rs 20000 d)Rs 24000
Answer :B
Explanation: Amount= Rs 30000 Time period T= 3 years
and Rate of interest= 25%
We have to find the principal P
A =P [ 1 +
R
100
]T =>30000= P[ 1 +
25
100
]3
=>30000=
P [
5
4
]3 => P= 30000 x
4
5
x
4
5
x
4
5
= Rs 15,360
On a sum of Rs 15,360, the amount we get in 3 years 25%
rate of compound interest is Rs 30000
6.
At what rate
percent compound interest, will Rs 20000
amount to Rs 22050 in 2 years?
a)
12% b)8% c)5% d)2%
Answer: C
Explanation:
Given that the amount is Rs 22050 And
Principal = Rs 20000
Time period T= 2 years
A =P [ 1 +
R
100
]T => 22050 = 20000[ 1
+
R
100
]2
ð $\frac{22050}{20000}$
= [ 1 +$\frac{R}{100}$
]2
ð $\frac{441}{400}$
=[ 1 +$\frac{R}{100}$
]2
ð ($\frac{21}{20}$
)2
= [ 1 +$\frac{R}{100}$
]2
ð $\frac{21}{20}$
= 1 +$\frac{R}{100}$
ð R=
5%
At 5% p.a compound interest, Rs 20000 becomes Rs 22050 in 2 years
7.
Find the
compound interest on Rs 32000 at 10% p.a for one and half years, the interest
being compounded half yearly?
a)Rs 5044 b)Rs
6000 c)Rs 3822 d)Rs 4000
Answer:A
Explanation:
Given Principal P= Rs 32000 Rate of
Interest =10% and Time period= one and half years = 1
1
2
years =
3
2
years
Amount= P[1 +
R/2
100
]2T => A = 32000 [ 1 +
10
200
]2 x 3/2
ð A=
32000 x $\left[\frac{21}{20}\right]
^{3} $
ð A=
32000 x $ \frac{21}{20}$
x $ \frac{21}{20}$ x $ \frac{21}{20}$
ð A
= 4 x21x21x21 =37044
Compound Interest = (Rs 37044 – Rs 32000) = 5044
8.
What is the
difference between the compound interest and the simple interest on Rs 12800 for 2
years at 10% p.a rate of interest?
a)
Rs 120 b)Rs 128 c)Rs
150 d)Rs 172
Answer:B
Explanation :
Simple Interest =
PTR
100
= 12800 X 2 X
10
100
= Rs 2560
To find compound interest, first we find the amount
Amount= P[1 +
R
100
]T = > 12800 x [ 1 +
10
100
]2 => 12800x
11
10
x
11
10
=15488
Compound interest = (A – P) => (Rs 15488 – 12800) = Rs
2688
The difference between CI and SI = (Rs 2688 – Rsd 2560) =
Rs 128
Short cut : The difference between CI and SI for 2
years at R% p.a is D =
PR2
1002
Therefore, D =
12800 X 102
1002
=
12800 X 10 X 10
100 X 100 2
= Rs 128
9.
The
difference between CI and SI on Rs 4000
for 2 years is Rs 10. What is the rate of interest per annum?
a)
2% b)7% c)9% d)5%
Answer: D
Explanation:
The difference between CI and SI for 2 years at R% p.a is D =
PR2
1002
ð R2
=
D x 1002
P
ð R2
= $\frac{10\times100\times100}{100}$
ð R=
5%
10. The difference between CI and SI on a certain sum of money for 3
years at 10% p.a rate of interest is Rs 1550. Find the principal?
a)
Rs 50000 b)Rs 34000 c)Rs
40000 d)Rs 42000
Answer : A
Explanation:
Shortcut method :When the difference between the simple
interest and THE compound interest on P for 3 years at R% rate of interest, then P
=
1003 x D
R2 X (300+R)
P=
100 x 100 x 100 x 1550
102 x (300+10)
P=
100x100x100x1550
100
x 310 = Rs 50000
11. The value of land increases by 15% annually. If its present
value is 1058000. What was its value 2 years ago?
a)
Rs 400000 b)Rs 500000 c)Rs
800000 d)Rs 1000000
Answer:C
Explanation:
Its present value is Rs 1058000
means; that is the amount.
A= P [ 1+
R
100
]T => Rs 1058000 = P [1+
15
100
]2
ð 1058000=
P [ $\frac{23}{20}$
]2
ð 1058000=
P X $\frac{529}{400}$
ð P
= 1058000 X $\frac{400}{529}$ = Rs 800000
12. At compound interest, a sum of money becomes 2 times itself in 4
years, In how many years will it become 8 times?
a)
10 years b)12 years c)14 years d)15 years
Answer: B
Explanation:
At compound interest, a principal is
always multiplied.
A sum
of money becomes 2 times in 4 years. Means every 4 years, the principal
becomes 2 times.
To become 8 times => 23 times (for each 2
times, it takes 4 years) , it takes (3 x 4) = 12 years
13. The compound interest on a certain sum of money for 2 years at
10% pa. Is Rs 2520. Find the simple
interest on the same sum of money at the same rate for 2 years?
a)
Rs 2000 b)Rs 2200 c)Rs 2400 d)Rs 2540
Answer:C
Explanation:
Given CI= Rs 2520 and and the rate of intest R = 10% and T= 2 years
Let Principal P
be Rs 100
=> Amount at
compound interest in 2 years
=> A = 100 x (
110
100
)2 => A= Rs 121
Theefore CI for 2 years is Rs 21
If P is Rs 100
---------CI is Rs 21
? ---------CI is Rs 2520
P =
2520
21
x 100 = Rs 12000
Now SI on Rs
12000 for 2 years at 10% rate of interest per annum => SI =
PTR
100
=> 12000 x 2 x
10
100
= Rs 2400
14. The SI on a certain sum of money for 3 years at 8% per annum is
Rs 1200. What is the compound interest
on the same sum of money at the same rate of interest for 2 years?
a) Rs 840 b)Rs
800 c)Rs 1000 d)Rs 832
Answer:D
Explanation:
Given SI= Rs 1200 T= 3 Years R= 8% T= 3 years
SI =
PTR
100
=> 1200 = P x
3 x
8
100
=> P = Rs 5000
To find CI, first we find Amount =>
A = P[ 1+
R
100
]T
ð A
= Rs 5000 x $\frac{108}{100}$
x $\frac{108}{100}$
= Rs 5832
Therefore, CI = (A –P)= (Rs 5832 – Rs
5000) = Rs 832
Shortcut
Method :
Given SI for 3 years is Rs 1200 . SI for 1 years is
Given SI for 3 years is Rs 1200 . SI for 1 years is
1200
3
= Rs 400
SI and CI are same for 1st
year.
Now CI for 2nd year = 400 +
8% on 1st year interest 400 = 432
CI
for 2 years = Rs 400+ Rs 432 = Rs 832
15. A sum of money amounts to Rs 2400 in 2 years and Rs 2640 in 3
years at CI. Find the rate of percent per annum?
a)10 % B)12$ C)12.5% D)14%
Answer:A
Explanation:
A1 = Rs 2400 and A2= 2640
(P + CI for 3 years) – (PI + CI for 2 years) = (Rs 2640 – Rs 2400)
= Rs 240
Rs 240 is the simple interest obtained on Rs 2400
in the 3rd year.
ð SI=
$\frac{PTR}{100}$
ð 240
= 2400 x 1 x $\frac{R}{100}$
ð R=
10%
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