Simple & Compound Interest — RRB NTPC Mathematics
This topic carries roughly 9% of Mathematics's 30 questions. It builds directly on Percentage (previous chapter) — interest calculations are percentage calculations applied repeatedly over time, with the compounding distinction being the one genuinely new idea.
1. What RRB NTPC actually asks
Expect direct SI and CI calculations, finding the principal/rate/time given the other values, the CI-SI difference for 2 years, and word problems (a sum doubling, tripling, or reaching a target amount).
2. Simple Interest
SI = (P × R × T) / 100, where P is principal, R is the annual rate, and T is time in years. SI is the same fixed amount every year, since it's always calculated on the original principal.
3. Compound Interest
CI amount A = P × (1 + R/100)^T. Compound interest = A − P. Unlike SI, each year's interest is calculated on the previous year's amount (principal + accumulated interest), not on the original principal alone — this is what makes it grow faster than SI over time.
4. The CI-SI difference shortcut (2 years)
For exactly 2 years, CI − SI = P × (R/100)². This one-step shortcut avoids computing both CI and SI amounts separately when only their difference is asked.
Worked examples
Q1. Find the compound interest on ₹8,000 for 2 years at 5% per annum, compounded annually.
Pick an option to check your answer.
Show explanation
Solution. Amount after year 1: 8000 × 1.05 = 8,400. Amount after year 2: 8,400 × 1.05 = 8,820. Compound interest = 8,820 − 8,000 = 820.
Alternatively via the shortcut: SI for 2 years = 8000 × 5 × 2/100 = 800; CI−SI = P(R/100)² = 8000 × 0.0025 = 20; so CI = 800 + 20 = 820, confirming the direct calculation. (a) is simple interest, not compound — the most common trap in this question type. Answer: (b).
Q2. The difference between compound interest and simple interest on a certain sum for 2 years at 10% per annum is ₹100. What is the sum?
Pick an option to check your answer.
Show explanation
Solution. Using the shortcut: CI − SI (2 years) = P × (R/100)². So 100 = P × (10/100)² = P × 0.01, giving P = 100/0.01 = 10,000.
Verify: SI on 10,000 for 2 years at 10% = 2,000. CI on 10,000 for 2 years at 10%: 10,000 × 1.1² = 12,100, so CI = 2,100. Difference = 2,100 − 2,000 = 100, matching exactly. Answer: (c).
6. Common traps
- Applying the SI formula when the question asks for CI, or vice versa. Read the question carefully — "compounded annually" or "compound interest" always means CI's exponential formula, never SI's flat-rate one.
- Computing CI by multiplying the rate by the number of years directly (as if it were SI). CI must be computed year-over-year (or via the exponent), since each year's base changes.
- Forgetting the CI-SI difference shortcut only applies to exactly 2 years. For 3 or more years, a different (more complex) formula applies, or year-over-year computation is safer.
- Confusing "amount" with "interest." The amount (A) includes the principal; interest (SI or CI) is A − P, the growth alone.
7. Guessing strategy
If a question mentions "compounded annually," any option matching the simple-interest value (P×R×T/100) is almost certainly a deliberately planted wrong answer — eliminate it immediately.
Summary
- Simple & Compound Interest is roughly 9% of Mathematics's 30 CBT 1 questions.
- SI = PRT/100, a fixed amount every year on the original principal.
- CI amount = P(1+R/100)^T; CI grows faster since each year compounds on the previous year's amount.
- For exactly 2 years, CI − SI = P(R/100)² — a one-step shortcut for a recurring question type.
- Always distinguish "amount" (includes principal) from "interest" (growth only, A − P).
- If a question specifies compounding, the flat SI-style answer is a common, deliberately planted distractor.
