Question 4 (a)

Equation of value: the final payment replacing two debts

6 marks

Time to write: About 12 minutes
Topic: Interest rates and compounding

Question

Question 4 (a) · 6 marks

Attempt any three questions, each carrying 6 marks.

A debt of ₹7200 due 9 years from now and ₹7200 due 15 years from now is to be repaid by a payment of ₹3600 in 2 years, a payment of ₹3600 in 4 years and a final payment at the end of 6 years. With the rate of interest at 8% compounded annually, how much is the final payment.

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

12 minfor 6 marks

Read from the question

any threeThe paper asks for any 3, and this is one of them. Only 3 are marked: a fourth earns nothing.
how muchFormula first, then the working, then the answer with its unit (₹, %, units).

What the paper leaves open

Q4 is "Attempt any three questions" of four parts (a) to (d); each part carries 6 marks, as printed.

Write it in this order

Read the data; note exactly what is asked 1 min
1 Equation of value at a focal date 2 marks 3 min
2 Values of the debts and payments 3 marks 5 min
3 Final payment 1 mark 2 min
Check: arithmetic, units (₹, %), final answer underlined 1 min

123

Short on time? Step 2 carries 3 of the 6 marks: guard its minutes.

Try it first. About 12 minutes for 6 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.

Equation of value. Take the date of the final payment, the end of year 6, as the focal date. At 8% compounded annually a sum moved forward t years is multiplied by (1.08)ᵗ and a sum moved back t years is divided by (1.08)ᵗ (A = P(1 + i)ⁿ; present value of a sum due later). The payments must equal the debts at that date:

3,600(1.08)⁴ + 3,600(1.08)² + X = 7,200(1.08)⁻³ + 7,200(1.08)⁻⁹

Working

At the end of year 6	Working	Value (₹)
Payment at year 2	3,600 × 1.360489	4,897.76
Payment at year 4	3,600 × 1.1664	4,199.04
Final payment X (balancing figure)		220.58
Debts: 7,200 due at year 9 + 7,200 due at year 15	7,200/1.259712 + 7,200/1.999005	9,317.38

Debts at year 6: 7,200/1.259712 = 5,715.59 and 7,200/1.999005 = 3,601.79, total ₹9,317.38.

X = 9,317.38 − 4,897.76 − 4,199.04 = ₹220.58.

The final payment at the end of 6 years is ₹220.58 (the two payments of ₹3,600, accumulated to year 6, almost cover the discounted value of the debts).

Check at the present time: PV of debts = 7,200/1.999005 + 7,200/3.172169 = 3,601.79 + 2,269.74 = ₹5,871.53; PV of payments = 3,600/1.1664 + 3,600/1.360489 + 220.58/1.586874 = 3,086.42 + 2,646.11 + 139.00 = ₹5,871.53.

Where the 6 marks sit

#	Component	Marks
1	Equation of value at a focal date	2
2	Values of the debts and payments	3
3	Final payment	1
	Total	6

Keyboard: ← → previous and next question, / search

Report a problemopens an email to admin@getkunji.com with the question ID832-Q4aalready filled in.