Simple and Compound Interest
Interest questions reward knowing exactly when interest is earned on the original principal alone versus when it compounds on top of itself.
10 questions · 5 minutes · instant scoring
What this topic actually tests
Simple interest (SI) is calculated only on the original principal for every period: SI = P x R x T / 100, where P is principal, R is the annual rate percent, and T is time in years. Compound interest (CI), by contrast, is calculated on the principal plus all previously accumulated interest, so the amount after T years is A = P x (1 + R/100)^T, and CI = A - P. For CLAT's typical 1-3 year compounding periods, it is often faster to compute the amount directly using the multiplying factor (1+R/100) raised to the power of T, rather than expanding the compound interest formula algebraically. A key shortcut: for exactly 2 years, CI always exceeds SI by P x (R/100)^2 — this is the 'interest on interest' for the second year alone, and it is worth deriving once so you can apply it directly instead of computing both CI and SI in full when a question only asks for their difference. When a sum is compounded more frequently than annually (half-yearly or quarterly), always convert the rate and time to match the compounding period before applying the formula: half-yearly compounding at annual rate R for T years means using rate R/2 per period for 2T periods, and quarterly compounding means using rate R/4 for 4T periods. Worked example: Rs 15,000 is invested for 1.5 years at 20% per annum, compounded half-yearly. The half-yearly rate is 10%, and there are 3 half-yearly periods in 1.5 years, so the amount is 15,000 x (1.10)^3 = 15,000 x 1.331 = Rs 19,965, and the compound interest earned is Rs 4,965 — noticeably more than simple interest would give, because more frequent compounding accelerates growth.
The common trap on this topic
The most common trap in this topic is applying the annual compounding formula directly to a half-yearly or quarterly compounding scenario without first adjusting both the rate and the number of periods — using the full annual rate for what should be a halved rate over doubled periods produces a significantly wrong, larger amount, since compounding more frequently at a proportionally smaller rate per period still compounds faster than annual compounding at the full rate. A second frequent trap is assuming compound interest can be calculated year by year using the same simple-interest-style formula applied repeatedly to the original principal, rather than recognising that each year's interest is calculated on the previous year's amount (principal plus accumulated interest) — this distinction is exactly what makes CI grow faster than SI, and skipping it produces an answer that is actually just simple interest restated. A third trap involves 'sum doubles/trebles in T years' questions: because SI = P x R x T/100 and doubling means SI = P (the interest equals the principal itself), students sometimes forget to substitute SI = P before solving for rate or time, instead treating the doubled amount 2P as the interest, which halves the correct rate.
Take the micro-test
Find the simple interest on Rs 8,000 at 6% per annum for 3 years.
A sum of Rs 5,000 amounts to Rs 6,500 in 4 years under simple interest. Find the annual rate of interest.
Find the compound interest on Rs 10,000 for 2 years at 10% per annum, compounded annually.
Find the difference between the compound interest and simple interest on Rs 5,000 for 2 years at 8% per annum (compounded annually).
At what annual rate of simple interest will a sum of money exactly double itself in 8 years?
A sum of Rs 12,000 is invested at 5% per annum compound interest, compounded annually, for 2 years. Find the final amount.
At what annual rate of simple interest will a sum of money treble (become 3 times) itself in 20 years?
The compound interest on a sum for 2 years at 10% per annum (compounded annually) is Rs 210. Find the sum.
A sum amounts to Rs 4,840 in 2 years at 10% per annum compound interest, compounded annually. Find the principal.
Find the compound interest on Rs 15,000 for 1.5 years at 20% per annum, compounded half-yearly.
FAQ
What is the core difference between simple and compound interest calculations?
Simple interest is calculated only on the original principal every period, so it grows linearly. Compound interest is calculated on principal plus all interest accumulated so far, so it grows on an increasing base — this is why CI always exceeds SI beyond the first compounding period, given the same principal, rate, and time.
Is there a shortcut for the difference between CI and SI over 2 years?
Yes — for exactly 2 years, CI minus SI always equals P x (R/100)^2, since this difference is just the interest earned in year two on the year-one interest alone. This is much faster than computing both CI and SI separately when only the difference is asked.
How do I handle half-yearly or quarterly compounding?
Halve the annual rate and double the number of years for half-yearly compounding (or take a quarter of the rate and quadruple the years for quarterly compounding) before applying the amount formula A = P(1+r/100)^n, where r and n are the adjusted per-period rate and number of periods.
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