A sum of money was lent for 2 years at 20% interest, compounded annually. If the interest is compounded half yearly, the interest would be 241 more. Find the sum. [Hint: take sum as 100 and find the interest.]
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answer is 10000
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Class 11
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>>Basics of financial mathematics
>>Accumulation with simple and compound interest
>>A sum of money was lent for 2 years at 2
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A sum of money was lent for 2 years at 20% compounded annually. If the interest is payable half-yearly instead of yearly, then the interest is Rs 485 more. Find the sum.
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Correct option is A)
Given, Rate (R)=20% per annum =
2
20
=10% half yearly
Time (n)=2 years =2×2=4 half years
Let P be the principal
According to the question,
⇒ P(1+
100
R
)
n
−P(1+
100
R
)
n
=482
⇒ P(1+
100
10
)
4
−P(1+
100
20
)
2
=482
⇒ P(
100
110
)
4
−P(
100
120
)
2
=482
⇒ P(1.4641)−P(1.44)=482
⇒ 0.0241P=482
⇒ P=
0.0241
482
∴ P=Rs.20000
∴ The sum is Rs.20,000