Question 1 OR (b)
Years needed for a deposit to grow to a target
7 marks
- Time to write
- About 14 minutes
From an older CBCS paper
Question
Question 1 OR (b) · 7 marksSuresh rented a house for 7 months, at a rent of Rs. 4,707 per month. Entire money is lying with him. Now he plans to invest it @ 9% p.a. so as to get Rs. 78,000. For how many years must the deposit be made to realise the amount desired? 7
Reworded from the university paper: names and figures differ, the task is the same. The original paper belongs to the University of Delhi. See DU's question bank.
Before you write
Read off the question and its marks
Read from the question
- how manyFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
"Entire money is lying with him" is read as the seven months' rent collected and held now; the deposit is that total, compounded at 9% annually.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Amount deposited 2 marks 3 min
- 2 Compound value formula and required factor 2 marks 3 min
- 3 Number of years, with check 3 marks 5 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Try it first. About 14 minutes for 7 marks. Write it out, then open the solution.
Solution
Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.
Amount deposited (paper note): the seven months' rent is held now: 7 × 4,707 = ₹32,949.
Compound value. A = P(1 + i)ⁿ, the general compounding formula with one compounding a year, so (1.09)ⁿ = 78,000 ÷ 32,949 = 2.3673.
From the compound value table at 9%, (1.09)¹⁰ = 2.367; by logarithms, n = log 2.3673 ÷ log 1.09 = 10.00 years.
Check: 32,949 × 2.367 = ₹77,990, about ₹78,000.
Where the 7 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Amount deposited | 2 |
| 2 | Compound value formula and required factor | 2 |
| 3 | Number of years, with check | 3 |
| Total | 7 |
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