A certain sum was lent at compound interest, compounded annually for three years. The rate of
interest for each of the three years was 20%, 15% and 10% p.a, respectively. If the same sum was lent
at a constant rate of simple interest for the same period, then what would have been the interest rate
for obtaining the same amount of interest?
(a) 17.27%
(b) 17%
(C) 18%
(d) 18.27%
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When interest is compounded, Amount A=P(1+
100
R
)
n
So, for the first year,
A
1
=P×(1+
100
5
)
1
=P×1.05=Rs1.05P
And interest for the first year I
1
=A−P=1.05P−P=0.05P
For the second year,
P
2
=1.05P
A
2
=1.05P×(1+
100
10
)
1
=1.05P×1.1=Rs1.155P
And interest for the second year I
2
=A
2
−P
2
=1.155P−1.05P=0.105P
For the third year,
P
3
=1.155P
A
3
=1.155P×(1+
100
12
)
1
=1.155P×1.12=Rs1.2936P
And interest for the second year I
3
=A
3
−P
3
=1.2963P−1.155P=0.1386P
Given, Total interest =Rs5284.80
=>0.05P+0.105P+0.1386P=Rs5284.80
=>0.2936P=Rs5284.80
=>P=Rs18,000
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