Find the amount and the compound interest on 20,480 for 1 1/2 years at 12 1/2 % per annum compounded half-yearly. Find the interest on the same principal for the same time period and at the same rate but calculated annually. Which interest is greater and by how much?
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The compound interest on Rs. 20,480 at 6
4
1
% per annum for 2 years 73 days, is
Medium
Solution
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Correct option is A)
Principal=20480Rs.
Time =2 years 73 days=2
5
1
years
interest rate
4
25
%
Amounnt after 2 years 73 days=20480(1+
4×100
25
)
2
(1+
100
5
1
×
4
25
)
⇒20480(1+
4×100
25
)
2
(1+
4×100
5
)
⇒20480(1+
16
1
)
2
(1+
80
1
)
⇒20480(
16
17
)
2
80
81
⇒
16×16×80
20480×17×17×81
⇒
16×16
256×17×17×81
⇒17×17×81=23409Rs.
Then C.I.=23409−20480=2929Rs.
Answer:
Principal=20480Rs.
Time =2 years 73 days=2
5
1
years
interest rate
4
25
%
Amounnt after 2 years 73 days=20480(1+
4×100
25
)
2
(1+
100
5
1
×
4
25
)
⇒20480(1+
4×100
25
)
2
(1+
4×100
5
)
⇒20480(1+
16
1
)
2
(1+
80
1
)
⇒20480(
16
17
)
2
80
81
⇒
16×16×80
20480×17×17×81
⇒
16×16
256×17×17×81
⇒17×17×81=23409Rs.
Then C.I.=23409−20480=2929Rs.
Step-by-step explanation:
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