Compound Interest
This page brings together the compound interest formula, its difference from simple interest, and solved examples for REET. The Financial Maths section brings a direct formula-based question from this topic almost every year.
- 1 question in REET 2024
- Class 8 level
- 8 min read
How REET asks this topic
REET 2024 asked a compound interest question where you had to find the time period (n) from the amount and principal — you had to rearrange the formula A = P(1+R/100)ⁿ and solve for the unknown. This shows that, besides straightforward formula-based calculation, the ability to solve for a variable is also tested here.
Definition and Core Formula
Compound Interest (CI) is interest that, at the end of each period, gets added to the principal to become the new principal for the next period — in other words, you earn interest on interest too. Simple Interest (SI), by contrast, is calculated on the original principal every single period.
If the principal is P, the annual rate is R%, and the time is n years, then the amount A = P(1 + R/100)ⁿ, and compound interest CI = A − P.
Important Formulas
- Annual compounding
- A = P(1 + R/100)ⁿ
- Half-yearly compounding
- A = P(1 + (R/2)/100)^(2n) — rate halved, time doubled
- Quarterly compounding
- A = P(1 + (R/4)/100)^(4n) — rate quartered, time quadrupled
- Difference between CI and SI (over 2 years)
- CI − SI = P × (R/100)² = PR²/10000
- Depreciation
- A = P(1 − R/100)ⁿ
Simple Interest (SI) vs Compound Interest (CI)
Simple Interest
How interest is calculatedAlways on the original principal
Type of growthLinear
In the first yearSI = CI (when compounding is annual)
FormulaSI = PRT/100
Compound Interest
How interest is calculatedOn the accumulated amount of each period
Type of growthExponential
In the first yearSI = CI (when compounding is annual)
FormulaA = P(1+R/100)ⁿ, CI = A−P
Solved Examples
Example 1: Find the compound interest on ₹5,000 at 10% per annum for 2 years. Solution: A = 5000 × (1.1)² = 5000 × 1.21 = ₹6,050. CI = 6050 − 5000 = ₹1,050.
Example 2 (PYQ-style): In how much time will ₹1,000 at 20% per annum earn ₹440 in compound interest? Solution: Amount A = 1000+440 = ₹1,440. 1440 = 1000 × (1.2)ⁿ ⇒ (1.2)ⁿ = 1.44 = (1.2)² ⇒ n = 2 years.
Example 3: Find the difference between CI and SI on ₹8,000 at 5% per annum for 2 years. Solution: Difference = P(R/100)² = 8000 × (5/100)² = 8000 × 0.0025 = ₹20.
Depreciation — Compounding at a Falling Rate
Just as an amount grows at a compound rate, the value of a machine, vehicle or property also falls by a fixed percentage each year, which is called depreciation. The formula is A = P(1 − R/100)ⁿ, where the minus sign shows that the value is falling, not rising.
Example: A machine currently worth ₹40,000 depreciates at 10% per year. What will it be worth after 2 years? Solution: A = 40000×(1−0.10)² = 40000×(0.9)² = 40000×0.81 = ₹32,400.
The same compound growth/decay formula applies to real-life situations like population growth, bank deposits, a company's profits, or the spread rate of a disease — which is why this topic goes well beyond pure financial maths and is genuinely useful in everyday life.
How to Teach This to Children
Classroom activity
Build a year-by-year table for an imaginary 'savings jar' growing bigger — each year, interest is added only on the previous year's total, so children see the exponential growth for themselves rather than just being handed the formula. Plotting SI and CI growth as two differently coloured lines on a graph also makes the difference visually clear.
Teaching aids
A year-wise growth table/graph and block models showing percentage growth are useful here.
Common misconception
Students often assume interest keeps being calculated on the original principal every year (as with simple interest), forgetting that in compound interest the base changes every year. Some students, in half-yearly/quarterly compounding, forget to adjust both the rate and the time and only adjust one, giving a wrong answer.
Assessment idea
Have students calculate both SI and CI for the same principal, rate and time, and compare — ask why and how much the difference grows. With older classes, you can also ask why the gap between CI and SI grows faster and faster as time increases, to build a deeper sense of exponential growth.
Memory trick / exam tip
In annual compounding, the simple interest and the compound interest for the first year are always equal — you can use this to check your calculation. Also, in 2-year questions, if you know the SI, save time by finding the difference directly with CI−SI = P(R/100)² instead of repeating the whole calculation.
REET 2024 Questions (with Solutions)
Question 100
In how much time will the interest on Rs. 1,000 be Rs. 440 at the rate of 20% annual compound interest ?
- A1 वर्ष
- B2 वर्ष
- C3 वर्ष
- D2 वर्ष 6 माह
Explanation
चक्रवृद्धि ब्याज 440 होने पर मिश्रधन = 1,000 + 440 = 1,440 रुपये। A = P(1 + R/100)ⁿ से 1,440 = 1,000 × (1.2)ⁿ, अर्थात् (1.2)ⁿ = 1.44 = (1.2)²। अतः n = 2 वर्ष।
Practice Questions
Question 1
Find the compound interest on ₹2,000 at 10% per annum for 1 year.
- A₹200
- B₹210
- C₹220
- D₹180
Explanation
In year 1 (with annual compounding), CI is always equal to SI. SI = 2000×10×1/100 = ₹200.
Question 2
Find the amount on ₹4,000 at 5% per annum compounded annually for 2 years.
- A₹4,410
- B₹4,400
- C₹4,200
- D₹4,500
Explanation
A = 4000×(1.05)² = 4000×1.1025 = ₹4,410.
Question 3
What is the compound interest on ₹1,600 at 25% per annum for 2 years?
- A₹900
- B₹800
- C₹750
- D₹850
Explanation
A = 1600×(1.25)² = 1600×1.5625 = ₹2,500. CI = 2500−1600 = ₹900.
Question 4
The compound interest on a sum for 2 years is ₹832 and simple interest is ₹800. Find the rate of interest.
- A8%
- B10%
- C5%
- D4%
Explanation
CI−SI = P(R/100)² = 32 and SI = PRT/100 ⇒ PR = 40000. Solving these gives R = 8% and P = ₹5,000 (check: SI=5000×8×2/100=800 ✓, CI=5000×1.1664−5000=832 ✓).
Question 5
At what annual rate will ₹1,000 amount to ₹1,210 in 2 years at compound interest?
- A10%
- B20%
- C5%
- D21%
Explanation
1210/1000 = 1.21 = (1.1)² ⇒ (1+R/100) = 1.1 ⇒ R = 10%.
Question 6
Find the compound interest on ₹10,000 at 10% per annum for 1.5 years, compounded half-yearly.
- A₹1,576.25
- B₹1,500
- C₹1,050
- D₹1,655
Explanation
Half-yearly rate = 5%, period = 3 (1.5×2). A = 10000×(1.05)³ = 10000×1.157625 = ₹11,576.25. CI = ₹1,576.25.
Question 7
The population of a village increases at 10% per annum. If the present population is 22,000, what will it be after 2 years?
- A26,620
- B26,400
- C24,200
- D27,000
Explanation
Population = 22000×(1.1)² = 22000×1.21 = 26,620.
Question 8
The difference between CI and SI on a certain sum for 2 years at 4% per annum is ₹1. Find the sum.
- A₹625
- B₹600
- C₹500
- D₹640
Explanation
CI−SI = P(R/100)² ⇒ 1 = P×(0.04)² = P×0.0016 ⇒ P = ₹625.
Question 9
A teacher builds a year-by-year interest table where each year's interest is added to the previous year's amount. This activity is most useful for clarifying which concept?
- Aब्याज की घातांकीय (exponential) वृद्धि
- Bकेवल मूलधन पर स्थिर ब्याज
- Cभिन्नों का योग
- Dप्रतिशत की परिभाषा
Explanation
When interest keeps getting added on the accumulated amount each year, growth becomes exponential — different from the linear growth of simple interest — and that's exactly the concept this activity makes clear.
Question 10
For the first year (annual compounding), the relationship between simple interest and compound interest is:
- Aदोनों बराबर होते हैं
- Bचक्रवृद्धि हमेशा अधिक होता है
- Cसाधारण हमेशा अधिक होता है
- Dकोई संबंध नहीं
Explanation
In the first year, compound interest is also calculated only on the original principal, so it equals the simple interest; the difference only starts to show from the second year onward.
Frequently Asked Questions
How many questions come from compound interest in REET?+
Usually 1 question from this topic appears, mostly as a formula-based calculation; REET 2024 also had 1 question.
What's the main difference between simple interest and compound interest?+
Simple interest is always calculated on the original principal, while compound interest is calculated on the accumulated amount of each period, so CI grows faster than SI over time.
What is the core formula for compound interest?+
A = P(1 + R/100)ⁿ, where CI = A − P. Here P is the principal, R the annual rate, and n the time (in years).
How does the formula change for half-yearly compound interest?+
In half-yearly compounding, the rate is halved (R/2) and the time doubled (2n): A = P(1+(R/2)/100)^(2n).
What's the relationship between SI and CI in the first year?+
In annual compounding, the simple interest and the compound interest for the first year are always equal; the difference only starts from the second year.
How is the depreciation formula related to compound interest?+
Depreciation uses the same type of formula as compound interest, just applied to a falling rate: A = P(1 − R/100)ⁿ, whereas compound growth gives A = P(1 + R/100)ⁿ.
What's the formula for the CI-SI difference over 3 years?+
For 3 years, CI−SI = P×R²×(300+R)/10⁶, which is different — and a bit more complex — than the 2-year formula P(R/100)².
What three quantities do you need to calculate compound interest?+
The principal (P), the annual interest rate (R), and the time (n, in years) — with these, the formula A = P(1+R/100)ⁿ gives the amount.
How do the rate and time change in quarterly compounding?+
In quarterly compounding, the annual rate is divided by 4 to get the quarterly rate, and the number of years is multiplied by 4 to get the number of quarters: A = P(1+(R/4)/100)^(4n).
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Change Log
- 17 September 2026 — English page published — mirrors the fact-checked Hindi page, independently bilingual-accuracy checked