Discussion
The present value of a bill due at the end of 2 years is Rs.1250. If the bill were due at the end of 2 years and 11 months, its present worth would be Rs.1200. Find the rate of interest and the sum.
Answer: B
The same bill \( A \) is being discounted over two different periods, so write each present worth in terms of \( A \) and the rate \( r \) (as a decimal).
\[ A = 1250(1 + 2r) \]
\[ A = 1200\left(1 + \tfrac{35}{12}r\right) \qquad \left(2 \text{ years } 11 \text{ months} = \tfrac{35}{12} \text{ years}\right) \]
Equating the two:
\[ 1250 + 2500r = 1200 + 3500r \]
\[ 50 = 1000r \quad\Longrightarrow\quad r = 0.05 = 5\% \]
\[ A = 1250(1 + 0.10) = \text{Rs. } 1375 \]
The longer the wait, the smaller the present worth - and the size of that drop over the extra 11 months is exactly what pins the rate down.
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