Question 1 (b)
Equal annual instalment on a loan
3 marks
- Time to write
- About 6 minutes
- Topic
- Time value of money
Question
Question 1 (b) · 3 marksTanvi takes a loan of ₹12,00,000 to be repaid in 5 equal instalments, one at the end of each year, at a rate of interest of 10%. Compute how much each instalment is.
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
- ComputeFormula first, then the working, then the answer with its unit (₹, %, units).
Write it in this order
- 1 Loan as the present value of an annuity 1 mark 2 min
- 2 Annuity factor and instalment 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.
The loan equals the present value of the five equal instalments at 10%, so the instalment is the loan divided by the present value annuity factor: PVA = A × annuity discount factor, hence A = 12,00,000 ÷ PVAF(10%, 5).
PVAF(10%, 5) = [1 − 1.10⁻⁵] ÷ 0.10 = 3.7908, the sum of the yearly factors 0.909 + 0.826 + 0.751 + 0.683 + 0.621 (3.790 from the table).
Annual instalment = 12,00,000 ÷ 3.7908 = ₹3,16,556.98 (with the 3-decimal table factor 3.791, about ₹3,16,539).
| Year | Opening balance | Interest @ 10% | Principal repaid | Instalment |
|---|---|---|---|---|
| 1 | 12,00,000.00 | 1,20,000.00 | 1,96,556.98 | 3,16,556.98 |
| 2 | 10,03,443.02 | 1,00,344.30 | 2,16,212.67 | 3,16,556.98 |
| 3 | 7,87,230.35 | 78,723.03 | 2,37,833.94 | 3,16,556.98 |
| 4 | 5,49,396.41 | 54,939.64 | 2,61,617.34 | 3,16,556.98 |
| 5 | 2,87,779.07 | 28,777.91 | 2,87,779.07 | 3,16,556.98 |
| Total | 3,82,784.88 | 12,00,000.00 | 15,82,784.88 |
The five instalments repay the ₹12,00,000 in full, with total interest of ₹3,82,784.88.
Where the 3 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Loan as the present value of an annuity | 1 |
| 2 | Annuity factor and instalment | 2 |
| Total | 3 |
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