Question 1 OR (a)
Accumulated value of equal yearly investments from today
3 marks
- Time to write
- About 6 minutes
- Topic
- Time value of money
Question
Question 1 OR (a) · 3 marksIf you begin investing a sum of ₹12,000 in mutual funds starting today, expecting to earn a return of 12% p.a., how much will you have accumulated in 10 years?
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 muchFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
"Start investing... starting today" is read as the sum being invested at the start of each year, beginning today, for 10 years (an annuity due), not as one lump sum. A single sum invested today is the other possible reading.
Write it in this order
- 1 Annuity-due reading and formula 1 mark 2 min
- 2 Future value computed 2 marks 4 min
Try it first. About 6 minutes for 3 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.
Reading (paper note). ₹12,000 is invested at the start of each year for 10 years, the first today: an annuity due.
The future value of an ordinary annuity (payments at the end of each year) is Sn = A × FVIFA(i, n). When each payment is made at the start of the year it earns interest for one more year, so the annuity-due value is Sn × (1 + i).
- FVIFA(12%, 10) = (1.12¹⁰ − 1) ÷ 0.12 = 17.5487.
- Ordinary annuity value: 12,000 × 17.5487 = ₹2,10,584.82.
- Annuity due: 2,10,584.82 × 1.12 = ₹2,35,855.00.
You will have about ₹2,35,855 after 10 years. (On the other reading, a single ₹12,000 invested today would grow to 12,000 × 1.12¹⁰ = ₹37,270.18.)
Where the 3 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Annuity-due reading and formula | 1 |
| 2 | Future value computed | 2 |
| Total | 3 |
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