DAV Class 8 Maths Chapter 6 Worksheet 3 Solutions: Compound Interest

Compound interest looks scary the first time you meet it, mostly because the numbers get long. But once you see that every question in this worksheet runs on the same small idea, the whole chapter becomes much easier. This article walks through all 19 questions of Worksheet 3 from the DAV Secondary Mathematics book for Class 8, one at a time, with the working shown so you can follow the logic and not just copy the answer.

The formulas you need before you start

Everything in this worksheet comes from one formula. If a sum P is invested for n years at a rate of R% per annum, compounded annually, then:

Amount A = P × (1 + R/100)^n

Compound Interest = A − P

When the interest is compounded half-yearly, the rate is halved and the number of years is doubled. So you use R/2 as the rate and 2n as the time. When it is compounded quarterly, you use R/4 as the rate and 4n as the time.

For simple interest, the formula you already know still applies: SI = (P × R × T) / 100.

For a sum lent for 2 years, the difference between CI and SI is P × (R/100)². For 3 years, the difference is P × (R/100)² × (3 + R/100). Questions 14 and 15 use this shortcut.

Questions 1 to 5: Finding amount and interest

Question 1. Find the amount for ₹15,000 at 8% per annum compounded annually for 2 years.

A = 15,000 × (1 + 8/100)²
A = 15,000 × (27/25)²
A = 15,000 × 729/625
A = 24 × 729 = ₹17,496

Answer: ₹17,496

Question 2. Find the compound interest on ₹11,200 at 17½% per annum for 2 years.

The rate 17½% is the same as 35/2%, so R/100 = 35/200 = 7/40.

A = 11,200 × (1 + 7/40)²
A = 11,200 × (47/40)²
A = 11,200 × 2209/1600
A = 7 × 2209 = ₹15,463

CI = 15,463 − 11,200 = ₹4,263

Answer: ₹4,263

A reader once pointed out that an earlier answer to this question was wrong on the source website, so it is worth double-checking this one in your own notebook.

Question 3. Ram borrowed ₹30,000 for 3 years at 6% per annum compounded annually. Find the interest he pays.

A = 30,000 × (1.06)³
(1.06)³ = 1.191016
A = 30,000 × 1.191016 = ₹35,730.48

Interest = 35,730.48 − 30,000 = ₹5,730.48

Answer: ₹5,730.48

Question 4. Nidhi deposited ₹7,500 at 4% per annum compounded annually. Find the amount and interest after 3 years.

A = 7,500 × (1.04)³
(1.04)³ = 1.124864
A = 7,500 × 1.124864 = ₹8,436.48

Interest = 8,436.48 − 7,500 = ₹936.48

Answer: Amount ₹8,436.48 and interest ₹936.48

Question 5. Find the difference between CI and SI on ₹30,000 at 7% per annum for 3 years.

First the compound interest.
A = 30,000 × (1.07)³ = 30,000 × 1.225043 = ₹36,751.29
CI = 36,751.29 − 30,000 = ₹6,751.29

Now the simple interest.
SI = (30,000 × 7 × 3) / 100 = ₹6,300

Difference = 6,751.29 − 6,300 = ₹451.29

Answer: ₹451.29

Questions 6 to 9: Comparing, and working backwards

Question 6. Aman borrows ₹14,500 at 11% for 3 years at simple interest. Tarun borrows the same amount at 10% for 3 years compounded annually. Who pays more interest and by how much?

Aman pays simple interest.
SI = (14,500 × 11 × 3) / 100 = ₹4,785

Tarun pays compound interest.
A = 14,500 × (1.1)³ = 14,500 × 1.331 = ₹19,299.50
CI = 19,299.50 − 14,500 = ₹4,799.50

Difference = 4,799.50 − 4,785 = ₹14.50

Answer: Tarun pays ₹14.50 more than Aman.

It is a nice little reminder that a lower compound rate can still cost more than a higher simple rate once enough years pass.

Question 7. The simple interest on a sum for 2 years at 5½% is ₹6,600. Find the compound interest on that sum at the same rate for the same time.

First find the sum from the simple interest.
6,600 = (P × 5.5 × 2) / 100
P = 6,600 × 100 / 11 = ₹60,000

Now the compound interest.
A = 60,000 × (1.055)² = 60,000 × 1.113025 = ₹66,781.50
CI = 66,781.50 − 60,000 = ₹6,781.50

Answer: ₹6,781.50

Question 8. A sum amounts to ₹2,970.25 in 2 years at 9% per annum compounded annually. Find the sum.

P × (1.09)² = 2,970.25
P × 1.1881 = 2,970.25
P = 2,970.25 / 1.1881 = ₹2,500

Answer: ₹2,500

Question 9. On what sum will the compound interest at 7½% per annum for 3 years be ₹3,101.40?

The amount factor is (1.075)³ = 1.242296875, so the interest factor is 0.242296875.

P × 0.242296875 = 3,101.40
P = 3,101.40 / 0.242296875 = ₹12,800

Answer: ₹12,800

If you prefer fractions, 7½% is 3/40, so the factor is (43/40)³ − 1 = 15,507/64,000, and the answer comes out the same.

Questions 10 to 13: Finding the rate or the time

Question 10. At what rate will ₹640 become ₹774.40 in 2 years?

(1 + R/100)² = 774.40 / 640 = 1.21
1 + R/100 = 1.1
R = 10%

Answer: 10% per annum

Question 11. At what rate will ₹64,000 become ₹68,921 in 3 years?

(1 + R/100)³ = 68,921 / 64,000 = 41³ / 40³
1 + R/100 = 41/40 = 1.025
R = 2.5%

Answer: 2½% per annum

Spotting that 68,921 is 41 cubed and 64,000 is 40 cubed makes this one quick.

Question 12. In how many years will ₹8,000 amount to ₹9,261 at 5% per annum compounded annually?

(1.05)ⁿ = 9,261 / 8,000 = 1.157625
Since (1.05)³ = 1.157625, n = 3

Answer: 3 years

Question 13. In what time will ₹3,750 at 20% per annum compounded annually amount to ₹6,480?

(1.2)ⁿ = 6,480 / 3,750 = 1.728
Since (1.2)³ = 1.728, n = 3

Answer: 3 years

Questions 14 and 15: Difference between CI and SI

Question 14. The difference between CI and SI on a sum at 6⅔% per annum for 3 years is ₹46. Find the sum.

Here R/100 = (20/3)/100 = 1/15.

Difference = P × (1/15)² × (3 + 1/15)
= P × (1/225) × (46/15)
= P × 46 / 3,375

So 46 = P × 46 / 3,375, which gives P = ₹3,375.

Answer: ₹3,375

Question 15. The difference between CI and SI on a sum at 15% per annum for 3 years is ₹283.50. Find the sum.

Here R/100 = 3/20.

Difference = P × (3/20)² × (3 + 3/20)
= P × (9/400) × (63/20)
= P × 567 / 8,000

So 283.50 = P × 567 / 8,000
P = 283.50 × 8,000 / 567 = ₹4,000

Answer: ₹4,000

Questions 16 to 19: Half-yearly and quarterly compounding

Question 16. Find the amount and compound interest on ₹12,800 for 1 year at 7½% per annum compounded semi-annually.

Half-yearly means the rate becomes 3.75% and the number of periods becomes 2.

A = 12,800 × (1.0375)²
= 12,800 × 1.07640625
= ₹13,778

CI = 13,778 − 12,800 = ₹978

Answer: Amount ₹13,778 and CI ₹978

Question 17. Mr Arora borrowed ₹40,960 at 12½% per annum compounded half-yearly. What will he pay after 1½ years?

The half-yearly rate is 6.25%, and 1½ years gives 3 periods.

A = 40,960 × (1.0625)³
Since 1.0625 = 17/16, A = 40,960 × 4,913 / 4,096
A = 10 × 4,913 = ₹49,130

Answer: ₹49,130

Question 18. Meera lent ₹20,000 for 9 months at 20% per annum compounded quarterly. What amount will she get?

The quarterly rate is 5%, and 9 months gives 3 quarters.

A = 20,000 × (1.05)³
= 20,000 × 1.157625
= ₹23,152.50

Answer: ₹23,152.50

Question 19. Find the amount and compound interest on ₹24,000 for 6 months if interest is payable quarterly at 20 paise a rupee per annum.

Twenty paise per rupee per year means 20% per annum. The quarterly rate is 5%, and 6 months gives 2 quarters.

A = 24,000 × (1.05)²
= 24,000 × 1.1025
= ₹26,460

CI = 26,460 − 24,000 = ₹2,460

Answer: Amount ₹26,460 and CI ₹2,460

Quick answer table

Q	Answer
1	₹17,496
2	₹4,263
3	₹5,730.48
4	₹8,436.48 amount, ₹936.48 interest
5	₹451.29
6	Tarun, ₹14.50 more
7	₹6,781.50
8	₹2,500
9	₹12,800
10	10%
11	2.5%
12	3 years
13	3 years
14	₹3,375
15	₹4,000
16	₹13,778 amount, ₹978 CI
17	₹49,130
18	₹23,152.50
19	₹26,460 amount, ₹2,460 CI

Mistakes students often make in this chapter

The most common slip is forgetting to subtract the principal at the end. The formula gives you the amount, not the interest, so always check what the question is actually asking for.

The second is mixing up the rate and time for half-yearly or quarterly questions. Halve or quarter the rate, and double or quadruple the time. Do both, never just one.

The third is writing a rate like 7½% as 7.2 or 7.12 by mistake. Convert it carefully to 7.5 or 15/2 before you begin.

Finally, when a question asks for the rate or the time, try to spot a perfect square or cube in the numbers, as in Questions 10 to 13. It saves a lot of long multiplication.

Frequently asked questions

Is the compound interest formula the same for every question in this worksheet?
Yes. Every question uses A = P(1 + R/100)ⁿ. Only the rate and the number of periods change when interest is compounded half-yearly or quarterly.

Why is compound interest more than simple interest?
Because in compound interest, each year’s interest is added to the principal, so the next year’s interest is calculated on a bigger amount. Simple interest always uses the original principal.

How do I find the principal when the amount is given?
Divide the amount by (1 + R/100)ⁿ, as shown in Questions 8 and 9.

Are these answers safe to use for homework?
Use them to check your own working. Try each question yourself first, then compare your steps and your final answer with the ones above.

Written for students following the DAV Secondary Mathematics book for Class 8. All answers were calculated and double-checked.