Chapter-2 (Compound Interest) Important Question

Compound Interest: Important Questions

Mathematics • Grade 10 • Theory and numerical questions with answers

Important Questions with Answers

Exam tips: (1) Write the formula first, then substitute. (2) For half-yearly use R/2 and 2T; for quarterly use R/4 and 4T. (3) For unknown rate or time, find CA ÷ P and compare it with (1 + R/100) powers. (4) For “two amounts” questions, divide one amount by the other.

A. Theory (short answer)

2 marks1. Define compound interest and compound amount.

If the interest is added to the principal after every fixed period and the next interest is calculated on the new principal, the total interest is compound interest. Principal + compound interest is the compound amount.

2 marks2. Write two differences between simple interest and compound interest.

• In SI the principal remains the same every year; in CI the principal increases every year (it equals the previous year’s amount).
• For the same P, R and T (more than one year) CI is greater than SI. For the first year they are equal.

3 marks3. Derive the formula for the compound amount after T years.

Interest after year 1 = PR/100, so A₁ = P + PR/100 = P(1 + R/100). This is the principal for year 2.

A₂ = A₁(1 + R/100) = P(1 + R/100)². Similarly A₃ = P(1 + R/100)³.

Continuing, CA = P(1 + R/100)^T and CI = CA − P.

2 marks4. Write the formulas for CA when interest is compounded (a) half-yearly, (b) quarterly, (c) for T years and M months.

(a) P(1 + R/200)^2T   (b) P(1 + R/400)^4T   (c) P(1 + R/100)^T(1 + MR/1200)

2 marks5. For the same sum, rate and time, arrange yearly, half-yearly and quarterly compound interest in increasing order. Why?

Yearly < half-yearly < quarterly. The more often interest is added to the principal, the more times interest is charged on interest. (Example: Rs. 1,00,000 at 15% for 1 year gives 15,000, 15,562.50 and 15,865.04.)

B. Numerical questions

3 marks6. A teacher borrowed Rs. 5,00,000 for 2 years at 12% p.a. and could not pay the first-year interest. Find the total interest.

I₁ = 60,000; P₂ = 5,60,000; I₂ = 67,200. Total interest = Rs. 1,27,200

3 marks7. Bishal paid simple interest and Badri compound interest on Rs. 30,000 for 3 years at 10%. Who pays more and by how much?

SI = 9,000. CI = 30,000[(1.1)³ − 1] = 9,930. Badri pays Rs. 930 more.

3 marks8. Find the CI and CA of Rs. 25,000 for 3 years at 12% yearly CI.

CA = 25,000(1.12)³ = 35,123.20. CI = Rs. 10,123.20 CA = Rs. 35,123.20

4 marks9. A man borrowed Rs. 32,000 at 12.5% SI and lent it at the same rate of CI for 3 years. How much more does he get?

SI = 12,000; CI = 13,562.50. Gain = Rs. 1,562.50

4 marks10. Rs. 5,000 is invested at 8% for 2 years. Compare half-yearly and yearly CI and suggest the better option.

Half-yearly CI = 5,000[(1.04)⁴ − 1] = Rs. 849.29. Yearly CI = Rs. 832. Half-yearly is better by Rs. 17.29.

4 marks11. Rs. 10,000 is invested at yearly CI; the amount after 1 year is Rs. 11,200. Find the rate and the amount after 2 years.

1 + R/100 = 1.12 ⇒ R = 12%. CA₂ = 10,000(1.12)² = Rs. 12,544

4 marks12. Find the CA and CI of Rs. 2,00,000 for 3 years if the rates are 8%, 10% and 12% in successive years.

CA = 2,00,000 × 1.08 × 1.10 × 1.12 = Rs. 2,66,112; CI = Rs. 66,112

4 marks13. A sum amounts to Rs. 14,520 in 2 years and Rs. 15,972 in 3 years at yearly CI. Find the rate and the principal.

1 + R/100 = 15,972/14,520 = 1.1 ⇒ R = 10%. P = 14,520/1.21 = Rs. 12,000

5 marks14. A bank lent Rs. 52,500 to Babulal and Jibanlal at 10% yearly CI. Babulal’s amount after 2 years equals Jibanlal’s after 3 years. Find each loan.

x(1.1)² = (52,500 − x)(1.1)³ ⇒ 2.541x = 69,877.5. Babulal Rs. 27,500 Jibanlal Rs. 25,000

5 marks15. Rs. 2,00,000 is deposited for 2 years at 10% p.a. half-yearly CI with 5% tax on interest. After 1 year the bank changes to quarterly compounding. Find the interest of each year after tax and the percentage difference.

Year 1 = Rs. 19,475. Year 2 = Rs. 21,645.12. Difference = Rs. 2,170.12, which is 11.14% of the first year’s interest.

3 marks16. Find the CI and CA: Rs. 64,000 for 3 years at 6% yearly CI.

CA = 64,000(1.06)³ = Rs. 76,225.02; CI = Rs. 12,225.02

3 marks17. At what yearly rate will the CI of Rs. 200 in 2 years be Rs. 42?

242/200 = 1.21 = (1.1)² ⇒ R = 10%

3 marks18. Find the CI and CA of Rs. 50,000 deposited for 3 years at 10% yearly CI.

CA = 50,000 × 1.331 = Rs. 66,550; CI = Rs. 16,550

4 marks19. Manisha deposits Rs. 50,000 at 8% half-yearly CI. Find the CI and CA after 2 years.

CA = 50,000(1.04)⁴ = Rs. 58,492.93; CI = Rs. 8,492.93

4 marks20. Find the difference between SI and CI of Rs. 80,000 at 8% for 2 years.

SI = 12,800; CI = 13,312. Difference = Rs. 512

4 marks21. Find the difference between the half-yearly and the yearly CI of Rs. 40,000 at 6% for 2 years.

Yearly CI = 4,944; half-yearly CI = 5,020.35. Difference = Rs. 76.35

5 marks22. A notice offers fixed deposit P: 10% half-yearly CI, and fixed deposit Q: 12% yearly CI. For Rs. 60,000 for 2 years, find the interest in each and say which to choose.

P: 60,000[(1.05)⁴ − 1] ≈ Rs. 12,930.38. Q: 60,000[(1.12)² − 1] = Rs. 15,264. Choose Q — it gives about Rs. 2,333.62 more.

4 marks23. If the yearly CI of a sum in 2 years at 15% is Rs. 180 more than the SI, find the sum.

P(0.15)² = 180 ⇒ P = Rs. 8,000

4 marks24. The half-yearly CI of a sum in 1 year at 10% is Rs. 40 more than the yearly CI. Find the sum.

0.1025P − 0.1P = 40 ⇒ 0.0025P = 40 ⇒ P = Rs. 16,000

4 marks25. At what rate does Rs. 700 amount to Rs. 847 in 2 years at yearly CI? And in how many years does Rs. 1,00,000 become Rs. 1,21,000 at 10%?

847/700 = 1.21 = (1.1)² ⇒ R = 10%. 1,21,000/1,00,000 = 1.21 = (1.1)² ⇒ T = 2 years

5 marks26. A sum becomes Rs. 10,580 in 2 years and Rs. 12,167 in 3 years at yearly CI. Find the rate and the sum.

12,167/10,580 = 1.15 ⇒ R = 15%. P = 10,580/(1.15)² = Rs. 8,000

5 marks27. The CI of a sum in the 1st year and in the first 2 years are Rs. 1,800 and Rs. 3,816. Find the rate and the sum.

2nd-year interest = 2,016. (2,016 − 1,800)/1,800 × 100 = 12%. P = 1,800/0.12 = Rs. 15,000

5 marks28. Rs. 80,000 is deposited for 2 years at 15% yearly CI with 5% tax on interest. After 1 year the bank changes to half-yearly compounding. By what percent does the second-year interest (after tax) differ from the first-year interest?

Year 1 after tax = Rs. 11,400. Year 2 after tax = Rs. 13,512.92. Difference = 18.53%

5 marks29. Ram divided Rs. 41,000 between his two daughters and deposited the parts at 5% yearly CI for 2 years and 3 years. If both receive equal amounts, find each part.

x(1.05)² = (41,000 − x)(1.05)³. Rs. 21,000 and Rs. 20,000

5 marks30. Divide Rs. 21,000 into two parts so that the CA of the first part for 3 years at 10% equals the CA of the second part for 2 years at 10%.

x(1.1)³ = (21,000 − x)(1.1)² ⇒ 2.1x = 21,000. Rs. 10,000 and Rs. 11,000

4 marks31. The CI of a sum for 1 year and 2 years are Rs. 450 and Rs. 945. Find the rate and the sum.

2nd-year interest = 495. (495 − 450)/450 × 100 = 10%. P = 450/0.10 = Rs. 4,500

4 marks32. Find the CA and CI of Rs. 50,00,000 for 1 year at 12% quarterly CI.

CA = 50,00,000(1.03)⁴ = Rs. 56,27,544.05; CI = Rs. 6,27,544.05

Compound Interest • Grade 10 Mathematics • Important Questions