Discussion
A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.482 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum.
Answer: D
\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]
Compare the two schemes over the same two years.
Yearly: \( P(1.2)^{2} = 1.44P \)
Half-yearly - 10% per half-year over four periods:
\[ P(1.1)^{4} = 1.4641P \]
\[ 1.4641P - 1.44P = 0.0241P = 482 \]
\[ P = \frac{482}{0.0241} = \text{Rs. } 20{,}000 \]
More frequent rests always earn a little more on the same nominal rate; here the gain is 2.41% of the principal.
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