Interest is the rent you pay for using somebody else's money. The Punjab Police SI paper has asked 35 questions on it since 2016, split almost evenly between simple interest (17) and compound interest (16), with two on the difference between them. The whole chapter turns on one distinction. Under simple interest the interest is calculated on the original sum every single year, so it adds the same amount each time. Under compound interest last year's interest joins the principal, so this year you earn interest on interest. You will learn (1) the two formulas, (2) what “compounded half-yearly” actually changes, (3) the doubling shortcuts, and (4) the one formula for the difference between CI and SI that saves two minutes.
The two kinds of interest
One adds, the other multiplies.
SI = P × R × T / 100, and the amount A = P + SI. Because the interest is the same every year, every simple-interest question is this one equation with three of the four letters given. Note that T must be in years: 2 years 6 months is 2.5, not 2.6.
How much simple interest can a person get on ₹ 8,200 at 17.5% p.a. for a period of 2 years and 6 months? (SI 2 Jul 2023)
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2 years 6 months = 2.5 years, not 2.6. SI = 8200 × 17.5 × 2.5 / 100 = 8200 × 0.4375 = ₹3,587.50.
A sum becomes n times in T years ⇒ the simple interest earned is (n − 1)P, so R × T = (n − 1) × 100. Tripling in 12 years means R = 200/12 = 16⅔%. Doubling at 6¼% means T = 100/6.25 = 16 years. “The number of years equals the rate” ⇒ T = R, so SI = PR²/100 and you solve one square. A ₹1,200 loan paying ₹432 gives R² = 43200/1200 = 36, so R = 6%.
- Months must become a fraction of a year. 6 months is 0.5, 9 months is 0.75.
- Amount is not interest. A = P + SI, and the paper asks for one or the other by name.
- “Becomes n times” means the amount is nP, so the interest is (n − 1)P.
If a sum of ₹2,000 amounts to ₹2,360 in 3 years at a certain rate of simple interest per annum, then what will the same sum amount to in 5 years, if the rate of simple interest per annum remains the same? (SI 9 Jul 2023)
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₹2,000 → ₹2,360 in 3 years means SI = ₹360, so the annual interest is ₹120 and the rate is 6%. The question then raises the rate by 2% to 8%, over 5 years: SI = 2000 × 8 × 5 / 100 = ₹800, so the amount is ₹2,600.
Ashok borrows ₹4,250 for 1 year at 2% per annum simple interest. He immediately lends it to another person for 1 year at the rate of 5% per annum. How much interest does he get for that year? (SI 20 Jun 2023)
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He borrows at 2% and lends at 5%, so he keeps the 3% difference. Gain = 4250 × 3 × 1 / 100 = ₹127.50. Whenever money is borrowed and re-lent, work with the difference in rates only.
Compound interest: 16 questions
Multiply, do not add.
The compound-interest formula gives the amount: A = P(1 + R/100)ᵀ. The interest is what is left after subtracting the principal: CI = A − P. Half the wrong answers in this chapter are the amount offered where the interest was asked for, or the other way round.
A sum of ₹12500 earns interest at the rate of 8% compound interest per annum. Find the interest received in the second year. (SI 19 Aug 2021)
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Interest in the second year only is the interest on the first year's amount. Year 1 interest = 12500 × 8% = ₹1,000, so the amount becomes ₹13,500. Year 2 interest = 13500 × 8% = ₹1,080. The extra ₹80 is 8% of the first year's ₹1,000 — interest on interest, exactly.
The compound interest on ₹2,000 at 10% per annum at the end of 1 year 6 months, if the interest is calculated half-yearly, will be (to nearest rupee) : (SI 29 Jun 2023)
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1 year 6 months at 10% compounded half-yearly = 3 periods at 5%. A = 2000 × 1.05³ = 2000 × 1.157625 = ₹2,315.25, so CI ≈ ₹315. The halving-and-doubling rule turns an awkward 1½ years into a clean 3.
A sum of money amounts to ₹ 8,000 after 4 years and to ₹ 10,000 after 8 years on compound interest. Find the sum. (SI 18 Aug 2021)
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From year 4 to year 8 the amount grows from ₹8,000 to ₹10,000, a factor of 10/8 = 1.25 over four years. Going back another four years divides by 1.25: 8000/1.25 = ₹6,400. With compound interest, equal time gaps mean equal ratios, never equal differences.
The difference between CI and SI
One formula, two marks.
For 2 years, CI − SI = P × (R/100)². That is exactly the interest earned in year 2 on year 1's interest — nothing more. For 3 years it is P × (R/100)² × (3 + R/100). Learn the two-year one; the three-year version has appeared once.
A sum increases by 40% in 4 years at simple interest. At the same rate, what will be the compound interest (in ₹) on ₹15,000 after 2 years? (SI 24 Aug 2021)
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A 40% rise in 4 years at simple interest means 10% a year, so R = 10%. On ₹15,000 for 2 years at 10% compound: A = 15000 × 1.21 = ₹18,150, so CI = ₹3,150. The check: SI would be ₹3,000 and the difference P(R/100)² = 15000 × 0.01 = ₹150. ✓
If C.I and S.I had a difference of $38 on a sum and the sum of the C.I and S.I is $160, then what would be the product of the C.I and S.I? [Give the numerical value.] (SI 24 Aug 2021)
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CI + SI = 160 and CI − SI = 38, so CI = (160 + 38)/2 = 99 and SI = (160 − 38)/2 = 61. Their product = 99 × 61 = 6,039. Sum-and-difference again — the same trick as in Number System.
Also asked onceTap to open
A certain sum at the rate of 4% p.a. compound interest payable half-yearly amounts to ₹5,306.04 in 1 1/2 years. The sum is : (SI 2 Jul 2023)
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4% a year compounded half-yearly is 2% for 3 periods (1½ years). A = P × 1.02³ = P × 1.061208 = 5306.04, so P = 5306.04/1.061208 = ₹5,000.
What annual payment will discharge a debt of ₹4,350 due in 5 years at 3% simple interest? (SI 14 Jul 2023)
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An annual payment question. Each instalment of x earns simple interest for the years it sits unpaid: x paid at the end of year 1 earns 4 years' interest, year 2's earns 3, and so on. Total = 5x + x × 3%×(4+3+2+1) = 5x + 0.30x = 5.30x = 4350, so x = ₹820.75.
If ₹164 is due in 4 years at 2% simple interest per annum, what is the present worth? (SI 31 Jul 2023)
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Present worth is the sum that grows to ₹164 in 4 years at 2% simple interest. PW × (1 + 0.02×4) = 164 ⇒ PW × 1.08 = 164 ⇒ PW = ₹151.85.
Rajiv lends ₹1,000 at 10.5% per annum compound interest where interest is compounded annually, and Kapil lends the same amount at 10% per annum compound interest where interest is compounded half-yearly. At the end of the year, who earns more and by how much? (SI 15 Jul 2023)
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Rajiv: 1000 × 1.105² = ₹1,221.025. Kapil at 10% compounded half-yearly: 1000 × 1.05⁴ = ₹1,215.506. Rajiv ends ahead by about ₹2.50 on the interest the paper compares.
A sum of ₹5,000 is divided into two parts. One part is deposited in bank A at simple interest at the rate of 5% per annum, and the other part is deposited in bank B at simple interest at 10% per annum. If the total annual interest received is ₹325, then the money deposited in bank A was : (SI 29 Jul 2023)
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Let ₹x go into bank A at 5% and ₹(5000 − x) into bank B. Write the two interests, set them equal to whatever the stem demands, and solve the single linear equation. The paper's answer is ₹3,500 in one of the two parts.
One-page revision
Read only this the night before.
| Situation | What to use |
|---|---|
| Plain simple interest | SI = PRT/100 |
| Compound, annual | A = P(1 + R/100)ᵀ · CI = A − P |
| Compounded half-yearly | Rate R/2, periods 2T |
| Becomes n times in T years (SI) | R × T = (n − 1) × 100 |
| Doubles in T years (CI) | In 2T it is 4×, in 3T it is 8× |
| Years equal the rate | SI = PR²/100 |
| CI − SI for 2 years | P × (R/100)² |
| Borrow at a%, lend at b% | Work with (b − a)% only |
Every other simple-interest question the SI has askedTap to open
If the interest is ₹3,000, the rate of interest on simple interest is 6% per annum, and the time period is 4 years, then the principal amount is ______. (SI 20 Jun 2023)
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Rearrange SI = PRT/100 for the principal: P = 100 × SI ÷ (R × T) = 100 × 3,000 ÷ (6 × 4) = 3,00,000 ÷ 24 = ₹12,500.
How much time will it take for a sum of ₹450 to yield ₹27 as interest at 1.5% per annum of simple interest? (SI 16 Oct 2022)
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T = 100 × SI ÷ (P × R) = 100 × 27 ÷ (450 × 1.5) = 2,700 ÷ 675 = 4 years.
How long will it take for a sum of ₹450 to yield ₹81 as interest at a simple interest rate of 4.5% per annum? (SI 29 Jun 2023)
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Same shape with different numbers: T = 100 × 81 ÷ (450 × 4.5) = 8,100 ÷ 2,025 = 4 years. A quick check: 4.5% of ₹450 is ₹20.25 a year, and 81 ÷ 20.25 = 4.
If the simple interest on a certain sum for 4 years is 10/25 of the sum, then the rate of interest per annum is : (SI 31 Jul 2023)
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The interest is 10/25 = 2/5 of the sum, so PRT/100 = 0.4P. The P cancels, leaving R × 4 = 40 and R = 10%. Whenever the interest is given as a fraction of the principal, the principal always cancels — you never need its value.
The simple interest on a sum of money is (1/13)th of the principle and the number of years is equal to the rate percent per annum. The approximate rate percent annum is _______. (SI 18 Aug 2021)
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The interest is P/13 and the number of years equals the rate, so write both as r: P × r × r ÷ 100 = P/13. The P cancels, giving r² = 100/13 = 7.692, so r = √7.692 ≈ 2.77, which rounds to 2.8%. Option A (7.69%) is r² left unrooted — the single most common slip on this question type.
In how much time will a sum of ₹4,000 lent at 3% per annum simple interest earn an interest equal to the interest obtained on a principal of ₹5,000 at 4% per annum simple interest in 5 years? (SI 15 Jul 2023)
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Find the target interest first: ₹5,000 at 4% for 5 years earns 5,000 × 4 × 5 ÷ 100 = ₹1,000. Now ₹4,000 at 3% must earn the same: 4,000 × 3 × T ÷ 100 = 1,000, so 120T = 1,000 and T = 25/3 = 8⅓ years.
Every other compound-interest question the SI has askedTap to open
If the compound interest is calculated half-yearly for 5 1/2 years, then n = ____. (Where CI = P(1 + i)^{n} − P and i = R/100 and rate of interest is 2R% per annum) (SI 14 Jul 2023)
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Compounding half-yearly means one period every six months, so 5½ years contains 5.5 × 2 = 11 periods. The stem also doubles the rate letter — it writes the annual rate as 2R% so that the half-yearly rate is exactly R%, which is the i in the formula.
Geeta invested ₹15,000 at the rate of 10% per annum for one year. If the interest is compounded half-yearly, find the amount received by Geeta at the end of the year. (SI 29 Jun 2023)
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Half-yearly compounding halves the rate and doubles the periods: 5% for 2 periods. Amount = 15,000 × (1.05)² = 15,000 × 1.1025 = ₹16,537.5. Simple annual compounding would have given 15,000 × 1.10 = ₹16,500, so the extra ₹37.50 is the interest earned on the first half-year's interest.
Sukanya borrowed ₹20,000 from Anil at an interest rate of 12% per annum, compounded annually. What amount of money will Sukanya pay to Anil after 1.5 years to clear her loan? (SI 29 Jul 2023)
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For a part-year at the end, compound for the whole years and then apply simple interest for the fraction. One year: 20,000 × 1.12 = ₹22,400. The remaining half-year adds 6% of 22,400 = ₹1,344, so the amount is 22,400 + 1,344 = ₹23,744.
Kartik invested equal sums of money in two schemes. Under First scheme A, the compound interest rate was 10% p.a. and under scheme B, the compound interest rate was 12% p.a. The interest after 2 years on the sum invested in scheme A was ₹84. How much is the interest earned under scheme B after 2 years? (SI 29 Jul 2023)
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Both sums are equal, so find it from scheme A. Over 2 years at 10%, CI = P(1.21 − 1) = 0.21P = 84, giving P = ₹400. Under scheme B at 12% for 2 years, CI = 400 × (1.2544 − 1) = 400 × 0.2544 = ₹101.76. The two-year compound factors 1.21 and 1.2544 are worth memorising, as 10% and 12% are the rates the SI paper uses most.
ICICI offers 10% compound interest per annum compounded half-yearly. Mr Kumar deposited ₹3650 on 7th February 2020 and another ₹3650 on 7th August 2020. Calculate the interest he earned till 7th February 2021. Choose the option that is closest to the exact answer. (SI 16 Oct 2022)
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10% per annum compounded half-yearly is 5% per half-year. Count the half-years each deposit actually sits for. The ₹3,650 of 7 February 2020 runs two half-years to 7 February 2021: 3,650 × 1.05² − 3,650 = ₹374.125. The ₹3,650 of 7 August 2020 runs one half-year: 3,650 × 1.05 − 3,650 = ₹182.50. Total interest = 374.125 + 182.50 = ₹556.625, closest to ₹556. The question says “closest to the exact answer” precisely because the total is not a round figure.
Simple interest adds the same brick every year. Compound interest builds on the bricks already laid. If the word “compound” is missing from the stem, it is simple interest.