Question 4 (a)

Compound amount under two successive rates and compounding periods

6 marks

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

Question

Question 4 (a) · 6 marks

Solve any three:

A man made a deposit of ₹3000 in a savings account. The deposit was left to accumulate at 8% compounded quarterly for the first 6 years and at 10% compounded semiannually for the next 9 years. Find the compound amount at the end of 15 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

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

What the paper leaves open

Q4 is "Solve any three" of five parts (a) to (e); each part is read as 6 marks, from the single marker printed after part (e).

Write it in this order

Read the data; note exactly what is asked 1 min
1 Rates and periods for each stage 2 marks 3 min
2 Amount after 6 years 2 marks 3 min
3 Amount after 15 years 2 marks 3 min
Check: arithmetic, units (₹, %), final answer underlined 2 min

123

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.

A = P(1 + i)ⁿ, where i is the rate per conversion period and n the number of conversion periods.

First 6 years at 8% compounded quarterly: i = 0.08/4 = 0.02 a quarter, n = 6 × 4 = 24 quarters. (1.02)²⁴ = 1.608437.

Amount after 6 years = 3,000 × 1.608437 = ₹4,825.31.

Next 9 years at 10% compounded semi-annually: i = 0.10/2 = 0.05 a half-year, n = 9 × 2 = 18 half-years. (1.05)¹⁸ = 2.406619.

Amount after 15 years = 4,825.31 × 2.406619 = ₹11,612.69.

Period	Rate per period	Periods	Factor	Amount at end (₹)
Years 1–6	2% a quarter	24	1.608437	4,825.31
Years 7–15	5% a half-year	18	2.406619	11,612.69

The compound amount at the end of 15 years is ₹11,612.69 (interest earned ₹8,612.69).

Where the 6 marks sit

#	Component	Marks
1	Rates and periods for each stage	2
2	Amount after 6 years	2
3	Amount after 15 years	2
	Total	6

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