Find the amount and the compound interest on 1600 for 2 years at the rate of 7.5% p.a.
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The difference between the compound interest and simple interest on a certain sum for 2 years at 7.5 % per annum is Rs. 360 . Find the sum.
Question
The difference between the compound interest and simple interest on a certain sum for 2 years at
7.5
%
per annum is Rs. 360. Find the sum.
Solution
Let sum (P) = Rs. 100
Rate (R)
=
7.5
%
=
15
2
%
p.a
Period (n) = 2 years
∴
C.I. = A - P
=
P
(
1
+
R
100
)
n
−
P
=
P
[
(
1
+
R
100
)
n
−
1
]
=
100
[
(
1
+
15
2
×
100
)
2
−
1
]
=
R
s
.
100
[
(
43
40
)
2
−
1
]
=
R
s
.
100
[
1849
1600
−
1
]
=
R
s
.
100
(
1849
−
1600
1600
)
=
R
s
.
100
×
249
1600
=
R
s
.
249
16
and S.I
=
P
R
T
100
=
100
×
15
×
2
100
×
2
=
R
s
.
15
∴
Difference in C.I and S.I
=
R
s
.
249
16
−
15
=
R
s
.
249
−
240
16
=
R
s
.
9
16
If difference is
9
16
, then sum = Rs. 100
if difference is Re. 1, then sum
=
R
s
.
100
×
16
9