A sum of $\rupee 2{,}000$ is invested at 7% per annum simple interest. Calculate the interests at the end of 1st, 2nd and 3rd year. Do these interests form an AP? If so, find the interest at the end of the 27th year.
Generated by claude-sonnet-4-6 · 2026-06-15 10:30 · grounding rag
Model Answer
Simple Interest formula: $\text{SI} = \frac{P \times R \times T}{100}$
Interest at end of 1st year $= \frac{2000 \times 7 \times 1}{100} = ₹140$
Interest at end of 2nd year $= \frac{2000 \times 7 \times 2}{100} = ₹280$
Interest at end of 3rd year $= \frac{2000 \times 7 \times 3}{100} = ₹420$
The interests are 140, 280, 420, …
Since $280 - 140 = 420 - 280 = 140$, the common difference is constant. Yes, they form an AP with $a = 140$ and $d = 140$.
Interest at end of 27th year:
$$a_{27} = a + (27-1)d = 140 + 26 \times 140 = 140 \times 27 = ₹3780$$
Source: Chapter 5, Section 5.3 (Example 9 pattern)
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Explanation
- This question is modelled exactly on Example 9 of Section 5.3, but with P = ₹2000, R = 7% instead of P = ₹1000, R = 8%.
- Examiners expect you to: (1) calculate the three interest values, (2) explicitly verify the AP by checking equal differences, and (3) apply $a_n = a + (n-1)d$ for the 27th term.
- Note: $a_{27} = 140 \times 27$ is a neat shortcut since $a = d = 140$.
- Do not confuse "interest at end of $n$th year" with total amount — it is only the SI for that cumulative time.