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State Board · Class 8 · Mathematics

Lesson 14: Compound Interest

2 concepts · 16 practice questions with answers · Free to read

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Recall: simple interest

From daily life

₹10,000 kept in a bank at 10 % for 3 years earns the same ₹1000 every year: ₹3000 in 3 years.

100000+1110001+1120002+1130003

In the figure: Simple interest: the same +1000 interest every year; after 3 years 10000 + 3000 = 13000.

Formula: Interest = Principal × Rate × Years ÷ 100 ; Amount = Principal + Interest

Live figure

Recall: simple interest

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  • Easy: Principal ₹6000, rate 5 %, 2 years: interest = 6000 × 5 × 2 ÷ 100 = ₹600; amount = ₹6600.
  • Medium: Principal ₹4000, rate 6 %, interest ₹720: years = 720 × 100 ÷ (4000 × 6) = 3 years.
  • Exam-type: After 3 years at 5 % the amount is ₹11,500: amount = principal × 1.15; principal = 11500 ÷ 1.15 = ₹10,000.
Remember

Simple interest is always on the original principal, so it is the same every year.

Common mistake

Mixing up interest and amount. Amount = principal + interest.

Shortcut

Rate × years = total percent. 5 % for 3 years is 15 % of the principal. Memory clue: Simple interest: principal × rate × years ÷ 100; remember the order "principal-rate-years".

Spot the difference

PointInterestAmount
Formulaprincipal × rate × years ÷ 100principal + interest
Meaningthe gaintotal money received back
₹1000, 5 %, 2 years₹100₹1100
Includes principalnoyes

Practice questions

Easy
  1. 1₹2000, 5 % rate, 3 years. Simple interest?
  2. 2₹8000, 10 % rate, 2 years. Simple interest?
  3. 3₹6000, 5 % rate, 4 years. Simple interest?
Medium
  1. 4Interest on ₹3000 for 3 years is ₹450. Rate?
  2. 5Interest on ₹5000 at 8 % is ₹1600. Years?
  3. 6At 5 % the amount after 3 years is ₹5750. Principal?
Challenging
  1. 7₹4000 becomes ₹4960 in 3 years. Rate of simple interest?
  2. 8₹6000 at 5 % for 2 years and ₹4000 at 10 % for 3 years: total simple interest?
Show answers (try them yourself first)
  1. 12000 × 5 × 3 ÷ 100 = ₹300.
  2. 28000 × 10 × 2 ÷ 100 = ₹1600.
  3. 36000 × 5 × 4 ÷ 100 = ₹1200.
  4. 4Rate = 450 × 100 ÷ (3000 × 3) = 5 %.
  5. 5Years = 1600 × 100 ÷ (5000 × 8) = 4.
  6. 6Amount = principal × 1.15; principal = 5750 ÷ 1.15 = ₹5000.
  7. 7Interest = 960; rate = 960 × 100 ÷ (4000 × 3) = 8 %.
  8. 8600 + 1200 = ₹1800.

Compound interest: interest on interest

From daily life

₹10,000 at 10 %: interest in year 1 is ₹1000. The principal becomes ₹11,000, so year 2 interest is ₹1100 on ₹11,000. Year 3 earns ₹1210 on ₹12,100. The interest grows every year.

Simple definition

When the interest earned at the end of each year is added to the principal and the next year’s interest is worked out on the new amount, it is compound interest.

100000+1110001+1.1121002+1.21133103

In the figure: Compound interest: growth gets bigger each year (+1000, +1100, +1210); after 3 years 13310.

Formula: Amount = Principal × (1 + Rate ÷ 100) × (1 + Rate ÷ 100) × … (once for every year) ; Compound interest = Amount − Principal

In words: At 10 % the amount becomes 1.10 times each year. In 3 years: 1.10 × 1.10 × 1.10 = 1.331 times.

Live figure

Compound interest: interest on interest

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  • Easy: ₹5000 at 10 % for 2 years. Amount = 5000 × 1.10 × 1.10 = 5000 × 1.21 = ₹6050 ; compound interest = 6050 − 5000 = ₹1050.
  • Medium: ₹16,000 at 5 % for 2 years. Amount = 16000 × 1.05 × 1.05 = 16000 × 1.1025 = ₹17,640 ; compound interest = ₹1640.
  • Exam-type: ₹8000 at 10 % for 3 years. Amount = 8000 × 1.331 = ₹10,648 ; compound interest = 10648 − 8000 = ₹2648 ; simple interest = 8000 × 10 × 3 ÷ 100 = ₹2400 ; difference = 2648 − 2400 = ₹248.
Remember

In compound interest the amount grows by the factor (1 + rate ÷ 100) every year.

Common mistake

Amount and interest are different. Amount = principal + interest; at the end CI = amount − principal.

Shortcut

Quick 2-year difference: CI − SI = Principal × (Rate ÷ 100)². E.g. ₹5000 at 10 %: 5000 × 0.01 = ₹50. (CI 1050, SI 1000, difference 50 ✔) Memory clue: Compound: every year multiply the amount by (1 + rate ÷ 100); "as many multiplications as years".

Spot the difference

PointSimple interestCompound interest
Interest onalways the original principalthe grown amount each year
Yearly interestsamekeeps growing
After 1 yearequalequal
After 2 yearslessmore

Practice questions

Easy
  1. 1₹4000 at 10 % for 2 years. Amount?
  2. 2Simple interest on ₹5000 at 10 % for 2 years?
  3. 3What is the difference between SI and CI after 1 year?
Medium
  1. 4₹10,000 at 20 % for 2 years. Compound interest?
  2. 5₹6000 at 5 % for 2 years. Difference between CI and SI?
  3. 6₹2500 at 4 % for 2 years. Amount?
Challenging
  1. 7On what principal does the amount become ₹12,100 in 2 years at 10 %?
  2. 8Compound interest on ₹10,000 for 3 years at 10 %? How much more than SI?
Show answers (try them yourself first)
  1. 14000 × 1.21 = ₹4840.
  2. 25000 × 10 × 2 ÷ 100 = ₹1000.
  3. 3No difference.
  4. 4Amount = 10000 × 1.2 × 1.2 = ₹14,400 ; CI = ₹4400.
  5. 56000 × 1.05 × 1.05 = ₹6615 ; CI = 615 ; SI = 6000 × 5 × 2 ÷ 100 = 600 ; difference ₹15.
  6. 62500 × 1.04 × 1.04 = ₹2704.
  7. 7Principal = 12100 ÷ 1.21 = ₹10,000.
  8. 8Amount = 10000 × 1.331 = ₹13,310 ; CI = ₹3310 ; SI = ₹3000 ; CI is ₹310 more.