Discussion
How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
Answer: A
\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]
Work out the two schemes separately over two years.
Yearly:
\[ 20000 \times (1.2)^{2} = 20000 \times 1.44 = \text{Rs. } 28{,}800 \]
Half-yearly - 10% per half-year over four periods:
\[ 20000 \times (1.1)^{4} = 20000 \times 1.4641 = \text{Rs. } 29{,}282 \]
\[ \text{difference} = 29282 - 28800 = \text{Rs. } 482 \]
The nominal rate is the same in both; only the frequency of the rests differs, and more frequent rests always earn more.
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