18. Find the rate of interest per annum, if 2000 amounts to 2315.25 in 1 years, , interest being compounded half yearly.
Answers
Answered by
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Step-by-step explanation:
Principal (P) = Rs. 2000
Amount (A) = Rs. 2315.25
Period (n)
=
1
1
2
years or 3 half-years.
Let R be a rate of half yearly, then
A
P
=
(
1
+
R
100
)
n
⇒
2315.25
2000
=
(
1
+
R
100
)
3
231525
100
×
2000
=
(
1
+
R
100
)
3
⇒
231525
100
×
2000
=
(
1
+
R
100
)
3
⇒
9261
8000
=
(
1
+
R
100
)
3
(Dividing by 25)
⇒
(
21
20
)
3
=
(
1
+
R
100
)
3
Comparing both sides, we get
1
+
R
100
=
21
20
=
1
+
1
20
∴
R
100
=
1
20
⇒
R
=
100
20
=
5
∴
Rate
=
5
%
half yearly or
10
%
p.a.
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