Find the difference between the C.I. and the S.I. for 2 years on a sum of Rs.8000 at 8% p.a. being compounded annually.
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11th
Applied Mathematics
Basics of financial mathematics
Accumulation with simple and compound interest
The difference between C.I ...
Maths
The difference between C.I and S.I for 2 years at 10% per annum is Rs.50. Find the sum.
Medium
Answer
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SI=
100
PRT
=
100
P×10×2
=
5
P
=0.2P
CI=A−P
=P(1+r)
t
−P
=P((1+0.1)
2
−1)
=P((1.1)
2
−1
2
)
=P(1.1+1)(1.1−1)
=P(2.1)(0.1)
=0.21P
CI−SI=0.21P−0.2P=50
=0.01P=50
=P=
0.01
50×100
=5000Rs.
solution
Answer:
We have,
P=Rs.8000,T=2 years,R=5%
We know that,
SI=
100
P×R×T
or, SI=
100
8000×5×2
or, SI=Rs.800
We know that,
A=CI+P=P(1+
100
R
)
T
or, CI+8000=8000(1+
100
5
)
2
or, CI+8000=8000(1+
20
1
)
2
or, CI+8000=8000(
20
21
)
2
or, CI+8000=8820
or, CI=Rs.820
Therefore, the required difference
CI−SI=820−800
=Rs.20