Install CompeteBits
Add to your home screen for one-tap access to mock tests & current affairs.
Study Materials › Arithmetic › Simple & Compound Interest
Interest questions are formula-driven and quick to score once you are careful with two things: the time unit and whether the rate compounds. Both 2022 papers included a question where the rate was quoted per quarter rather than per year — a detail that changes the whole answer.
Simple Interest = P × T × R / 100
Amount (SI) = P + SI = P (1 + TR/100)
Amount (CI) = P (1 + R/100)T
Compound Interest = P [ (1 + R/100)T − 1 ]
Depreciation = P (1 − R/100)T (compounding downwards)
For 2 years: CI − SI = P (R/100)2
For 3 years: CI − SI = P (R/100)2 × (3 + R/100)
These two lines save a great deal of time. Any question that gives you the difference and asks for the principal is a one-step substitution.
| Compounded | Rate to use | Time to use |
|---|---|---|
| Annually | R | T years |
| Half-yearly | R / 2 | 2T |
| Quarterly | R / 4 | 4T |
A person invested ₹18,000 at 20% compound interest per annum. Find the interest after two years.
Amount = 18000 × (1.20)2 = 18000 × 1.44 = 25,920.
Interest = 25,920 − 18,000 = ₹7,920.
At the rate of 2% per quarter of a year, the simple interest after 24 months is ₹960. Find the principal.
24 months = 8 quarters, and the rate is 2% per quarter, so the total rate over the period is 16%.
0.16 × P = 960, giving P = ₹6,000.
Trap: reading "2% per quarter" as 2% per year gives ₹24,000 — and that style of wrong
answer is usually sitting right there in the options.
A person invested ₹X at 18% simple interest and ₹Y at 12% simple interest, receiving ₹4,320 interest in a year. Had the amounts been interchanged, he would have received ₹4,680. Find |X − Y|.
0.18X + 0.12Y = 4320 …(i)
0.12X + 0.18Y = 4680 …(ii)
Adding: 0.30 (X + Y) = 9000, so X + Y = 30,000.
Subtracting (ii) from (i): 0.06 (X − Y) = −360, so X − Y = −6,000.
Therefore |X − Y| = ₹6,000.
Note: whenever a question interchanges two investments, adding and subtracting the two equations
is almost always faster than solving them individually.
A building initially worth ₹31,25,000 depreciates at 4% per year. Land initially worth ₹32,00,000 appreciates at 5% compounded. If x is the building's value and y the land's value after 3 years, find y − x.
Building: 31,25,000 × (0.96)3 = 31,25,000 × 0.884736 = 27,64,800.
Land: 32,00,000 × (1.05)3 = 32,00,000 × 1.157625 = 37,04,400.
y − x = 37,04,400 − 27,64,800 = ₹9,39,600.
Note: depreciation is just compound interest with a minus sign — same formula, (1 − R/100).
Also see: Percentages · Profit & Loss · Time & Work