Question 1 OR (b)

Present value of a deferred annuity

7 marks

Time to write
About 14 minutes

From an older CBCS paper

Question

Question 1 OR (b) · 7 marks

Mr. Sunil is to receive ₹ 9600 a year for eight consecutive years, but the receipts would start third year from now. If the required rate of return is 12%, find the present value of the sum received. 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

14 minfor 7 marks

Read from the question

  • findFormula first, then the working, then the answer with its unit (₹, %, units).

What the paper leaves open

"Start third year from now" is read as: the first receipt comes at the end of year 3.

Write it in this order

  1. Read the data; note exactly what is asked 1 min
  2. 1 Reading of the deferral 2 marks 3 min
  3. 2 Value at the end of year 2 2 marks 3 min
  4. 3 Discounting to today, with check 3 marks 5 min
  5. 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.

Reading (paper note): the first receipt comes at the end of year 3 and the last at the end of year 10. The annuity is therefore deferred by 2 years: find its value at the end of year 2, then discount that to today.

Step 1. Value at the end of year 2. PVIFA (12%, 8 years) = 4.968: 9,600 × 4.968 = ₹47,692.80.

Step 2. Discount to today. PVF (12%, 2 years) = 0.797: 47,692.80 × 0.797 = ₹38,011.16.

Check by the difference of annuity factors. PVIFA (12%, 10) − PVIFA (12%, 2) = 5.650 − 1.690 = 3.960; 9,600 × 3.960 = ₹38,016. The small difference comes from rounding the table factors.

Present value of the receipts ≈ ₹38,011.

Where the 7 marks sit

#ComponentMarks
1Reading of the deferral2
2Value at the end of year 22
3Discounting to today, with check3
Total7
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