Simple and Compound Interest is one of the most predictable scorers in AFCAT Numerical Ability — nearly every paper carries a direct sum, and the logic feeds Percentage, Growth and Population questions too. The whole topic rests on one idea: how money grows on a principal over time at a given rate. This Cavalier guide builds each formula from scratch and hands you the speed tricks that win real seconds.
Why Simple and Compound Interest is a must-score topic
Interest is the rent paid for the use of money. When you lend or deposit a principal, it earns extra money called interest over a period of time at a fixed rate per cent per annum. AFCAT examiners love this chapter because the idea is everyday — bank deposits, loans, EMIs — yet the same numbers can be wrapped in many disguises.
For AFCAT, this chapter overlaps heavily with Percentage, Ratio and Growth, so the work you do here pays off across the whole Numerical Ability section. Most questions are one-step or two-step once you decide whether the interest is simple or compound.
At The Cavalier we tell our defence aspirants to treat Interest as a guaranteed booster: the data is friendly, the formulas are short, and a calm reader rarely loses marks. The only real enemies are mixing up the two interest types and fumbling the time when compounding happens more than once a year.
In Simple Interest the principal stays fixed every year. In Compound Interest each year's interest is added to the principal, so the next year earns interest on a bigger base. That single difference drives the entire chapter.
The core terms and the Simple Interest formula
Four quantities run through every sum in this topic. Fix them firmly before touching formulas.
- Principal (P) = the original sum lent, borrowed or invested.
- Rate (R) = interest charged per ₹100 per year (per cent per annum).
- Time (T) = the period, always taken in years for the basic formula.
- Amount (A) = Principal + Interest, the total finally repaid.
The headline Simple Interest formula is the one examiners test most:
SI = (P × R × T) ÷ 100
Amount A = P + SI = P × (1 + RT÷100)
Because SI grows by the same amount every year, the interest is directly proportional to time. Double the time and you double the interest; treble the rate and you treble it. Identifying which of P, R, T or SI is missing — before you calculate — stops you solving the wrong thing under exam pressure. Rearranging the single SI formula gives you every other quantity: P = 100×SI÷(R×T), R = 100×SI÷(P×T), and T = 100×SI÷(P×R).
Find the simple interest on ₹5,000 at 8% per annum for 3 years.
The Compound Interest formula
In compound interest each year's interest is added back to the principal, so growth speeds up year on year. The amount after T years is found in one step.
Amount A = P × (1 + R÷100)T
Compound Interest CI = A − P = P × [(1 + R÷100)T − 1]
Turn the rate into a growth factor and multiply. A 10% rate means each year the money becomes 1.10 times itself; for 2 years multiply by 1.10 twice, i.e. 1.21. No yearly addition needed.
Find the compound interest on ₹8,000 at 10% per annum for 2 years.
Do not multiply SI by the number of years and call it CI. Compound interest needs the power formula; for 2 years at 10% it is ₹1,680, whereas simple interest would be only ₹1,600.
The growth-factor habit is one of the biggest time-savers in the paper. Once you stop thinking “find each year's interest and add it” and start thinking in terms of a single factor like 1.10 or 1.05 raised to the time, multi-year questions collapse into one quick multiplication. Practise the common squares — (1.1)2 = 1.21, (1.2)2 = 1.44, (1.05)2 = 1.1025 — until they come instantly.
Half-yearly and quarterly compounding
When interest is compounded more than once a year, you adjust both the rate and the time. The rate is divided and the number of periods is multiplied.
Half-yearly: rate becomes R÷2, time becomes 2T → A = P × (1 + R÷200)2T
Quarterly: rate becomes R÷4, time becomes 4T → A = P × (1 + R÷400)4T
More frequent compounding always yields slightly more interest, because money is reinvested sooner. So half-yearly CI > yearly CI for the same nominal rate.
Find the amount on ₹10,000 at 10% per annum compounded half-yearly for 1 year.
Keeping the rate at 10% and the time at 1 for half-yearly sums is wrong. You must halve the rate to 5% and double the periods to 2 before applying the power formula.
The CI minus SI difference shortcuts
A classic AFCAT type asks for the difference between compound and simple interest on the same principal, rate and time. Ready-made formulas make this almost instant.
For 2 years: CI − SI = P × (R÷100)2
For 3 years: CI − SI = P × (R÷100)2 × (3 + R÷100)
The 2-year difference is simply “simple interest on one year's interest.” It equals P×R2÷10000, so for ₹5,000 at 10% it is 5000×100÷10000 = ₹50 — done mentally.
Find the difference between CI and SI on ₹12,000 at 5% per annum for 2 years.
This difference arises only because compound interest charges “interest on the interest.” In year one both are equal; the gap opens from year two onward. Memorising the 2-year and 3-year formulas lets you answer a whole family of questions without ever computing the two interests separately, which is exactly the time-saving the examiner is testing.
Rate fractions and the assume-100 method
Many AFCAT sums hide the money values and only give rates, or use awkward fractional rates. Treating a rate as a clean fraction skips heavy arithmetic.
Convert common rates to fractions: 12½% = 1÷8, 6¼% = 1÷16, 8⅓% = 1÷12, 16⅔% = 1÷6, 20% = 1÷5. The interest then becomes a simple fraction of the principal.
Find the simple interest on ₹6,400 at 12½% per annum for 1 year.
When a question gives only percentages and no money, assume P = ₹100 (or a convenient multiple of 100). Every figure then turns into an easy percentage and the answer reads off directly.
The fraction habit is especially powerful in compound interest, where each year the principal is multiplied by (1 + fraction). A 25% rate, for instance, means multiply by 5÷4 each year, so after two years the amount is (5÷4)2 = 25÷16 of the principal — clean numbers with no decimals to slip on.
Equal-amount and installment problems
Another high-frequency type: a sum is lent so that two people (or two time periods) repay equal amounts, or a debt is cleared in equal annual installments. Both reduce to the amount formula.
If a sum is repaid in equal annual installments under compound interest, the present value of each installment is Installment ÷ (1 + R÷100)n, and the principal equals the sum of these present values.
A sum of ₹2,550 is to be paid in two equal annual installments at 4% per annum simple-style compounding. Roughly, what is each installment? (Use CI.)
The key insight is that each installment, when discounted back to today using the growth factor, must add up to the original loan. Whenever a question mentions “equal annual installments” or “repaid in n equal parts,” reach for the present-value idea rather than guessing. For two installments the algebra is short; for three it is the same pattern with one more term.
Doubling, tripling and the time-to-grow trap
A favourite AFCAT trap asks how long a sum takes to double or triple. Under simple interest the logic is linear and easy to extend.
Under SI, if money doubles in T years then SI = P, so R×T = 100. The time to triple (SI = 2P) is exactly double the doubling time; to become 4 times, three times the doubling time.
At what rate of simple interest will a sum double itself in 8 years?
Under compound interest the doubling time does not scale linearly. If a sum doubles in 4 years under CI, it becomes 4 times (not 3 times) in 8 years, because 2×2 = 4. Watch which interest type the question states.
For SI, “n times in T years” means SI = (n−1)P, giving R×T = 100(n−1). For CI, repeated multiplication governs growth, so doubling twice over equal periods means the money squares each time — a very different and very commonly tested distinction.
Population, growth and depreciation links
The compound interest formula is the engine behind population growth, appreciation and depreciation questions too, so the same skill scores in those topics.
Population after n years = P × (1 + r÷100)n for growth.
Depreciated value = P × (1 − r÷100)n for a fall in value.
The value of a machine worth ₹50,000 depreciates 10% each year. Find its value after 2 years.
Notice the only change from compound interest is the sign inside the bracket: a plus for growth and a minus for depreciation. If a population first rises one year and falls the next, multiply the two factors together — exactly the successive-change idea you use in Percentage. Recognising that all of these are the same compound formula in disguise means one mastered tool answers four different question types in the paper.
Previous-year style question
Q. The difference between the compound interest and the simple interest on a certain sum at 10% per annum for 2 years is ₹40. Find the sum.
Answer: For 2 years, CI − SI = P × (R÷100)2. So 40 = P × (10÷100)2 = P × (1÷100). Therefore P = 40 × 100 = ₹4,000. The required sum is ₹4,000.
Traps and time-savers to keep in mind
- Treating compound interest like simple interest by just multiplying SI by the years.
- Forgetting to halve the rate and double the periods for half-yearly compounding.
- Using the 2-year difference formula on a 3-year sum — the 3-year one has an extra factor.
- Assuming CI doubling time scales linearly the way SI doubling time does.
Always assume P = ₹100 when the question gives only rates and times. Every interest figure then becomes a clean percentage, and the final answer reads off directly. This single habit speeds up most rate-only problems.
Quick revision
- SI = P×R×T÷100; Amount = P + SI; interest is the same every year.
- CI: A = P×(1 + R÷100)T; CI = A − P.
- Half-yearly: rate R÷2, periods 2T; quarterly: rate R÷4, periods 4T.
- 2-year difference: CI − SI = P×(R÷100)2.
- 3-year difference: P×(R÷100)2×(3 + R÷100).
- SI doubling: R×T = 100; CI growth multiplies year on year.
- Use rate fractions (12½% = 1÷8) and assume P = ₹100 when only rates are given.
Frequently asked questions
What is the main difference between simple and compound interest?
In simple interest the principal stays fixed, so each year earns the same interest. In compound interest each year's interest is added to the principal, so the next year earns interest on a larger base. Compound interest therefore always exceeds simple interest beyond the first year.
How do I adjust the formula for half-yearly compounding?
Halve the rate and double the number of periods. For R% per annum over T years compounded half-yearly, use A = P times (1 + R/200) raised to the power 2T. Quarterly compounding uses R/4 and 4T.
What is the quickest way to find the difference between CI and SI for 2 years?
Use CI minus SI = P times (R/100) squared. It equals simple interest on one year's interest. For example, on 5,000 rupees at 10% for 2 years the difference is 5000 times (10/100) squared = 50 rupees.
If a sum doubles in 8 years under simple interest, when does it triple?
Under simple interest the interest is linear, so the time to triple is double the doubling time. If it doubles in 8 years it triples in 16 years. This linear scaling does not hold for compound interest.
What is the fastest approach when a question gives only rates and no money?
Assume the principal is 100 rupees, or a convenient multiple of 100. Every interest figure then becomes a simple percentage, and using rate fractions like 12 and a half percent equals one-eighth keeps the arithmetic clean and fast.
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