the difference between compound interest and simple interest on an amount pf ₹15000 for 2 years is ₹96. what the rate of interest per annum
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Answer:
R = 8%
Step-by-step explanation:
Given that, principal,
P
=
₹
15000
and time period,
n
=
2
years .
Let the rate of interest per annum be
r
.
Simple interest in 2 years
S
.
I
=
15000
×
r
×
2
100
⇒
S
.
I
=
300
r
Compound interest
C
.
I
=
A
−
P
=
15000
(
1
+
r
100
)
2
−
15000
, here,
A
is the amount.
In compound interest, the interest is calculated on the amount of the previous year. Therefore it is known as interest compounded or Compound Interest (C.I.)
We know that after the first year, C.I > S.I
Given that
C
.
I
−
S
.
I
=
96
(Since C.I > S.I)
⇒
15000
(
1
+
r
100
)
2
−
15000
−
300
r
=
96
⇒
15000
(
1
+
r
100
)
2
−
300
r
=
15096
⇒
15000
(
1
+
r
2
10000
+
2
r
100
)
−
300
r
=
15096
⇒
15000
+
15
r
2
10
+
300
r
−
300
r
=
15096
⇒
15
r
2
10
=
96
⇒
15
r
2
=
960
⇒
r
2
=
64
⇒
r
=
±
8
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