the different between the simple and compound interest on a certain sum of money for 4 years at 6% p.a is rs 168.75. what is the sum?
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Explanation:
Let the principle is P and rate of interest is 15%.
Time =2 years
Then, for CI:
CI =P(1+
100
R
)
2
−P
CI =P[(1+
100
15
)
2
−1] ......[∵(a+b)
2
=a
2
+b
2
+2ab]
⇒ CI =P[1+
100
2×15
+
10000
(15)
2
−1]
⇒ CI =P[1+
100
30
+
10000
225
−1]
⇒ CI =P[
10
3
+
400
9
]
⇒ CI =P[
400
120+9
]
CI =
400
129P
For SI:
⇒ SI =
100
PRT
⇒ SI =
100
P×15×2
⇒ SI =
100
30P
According to the question, we have
CI−S.I=Rs.144
⇒
400
129P
−
100
30P
=144
⇒
400
129P−120P
=144
⇒P=
9
144×400
P= Rs. 6400
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