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Question : A sum was lent for one year at the rate of 16 percent per annum on compound interest (compounding annually). If the compounding had been done half yearly, then the interest would have increased by Rs. 64. What was the sum lent?

Option 1: Rs. 10000

Option 2: Rs. 6000

Option 3: Rs. 14000

Option 4: Rs. 20000


Team Careers360 3rd Jan, 2024
Answer (1)
Team Careers360 22nd Jan, 2024

Correct Answer: Rs. 10000


Solution : We know, Total Amount = Principal × (1 + $\frac{\text{Rate}}{100})^{\text{Time}}$
Let the lending amount be $x$.
⇒ Interest earned with annually compounding
= $x (1 + \frac{16}{100}) - x$
= $x \times\frac{116}{100} - x$
= $\frac{116x}{100}-x$
⇒ Interest earned with half-yearly compounding
= $x (1 + \frac{16}{200})^2- x$
= $x(1+\frac{2}{25})^2-x$
= $x(\frac{27}{25})^2- x$
Given,
The difference in interest earned is Rs. 64.
⇒ $[x(\frac{27}{25})^2- x] - [\frac{116x}{100}-x] = 64$
⇒ $x[\frac{729}{625}-\frac{116}{100}]=64$
⇒ $x[\frac{729}{625}-\frac{29}{25}]=64$
⇒ $x(\frac{729-725}{625}) = 64$
⇒ $x\times\frac{4}{625}=64$
⇒ $x = \frac{64}{4}\times625= 10000$
Hence, the correct answer is Rs. 10,000.

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