The difference of compound interest and simple interest of a sum of money at the rate of 5% per year for 2 years is ₹250. The sum is
- (a)₹1,00,000
- (b)₹80,000
- (c)₹40,000
- (d)₹1,20,000
Correct — A, ₹1,00,000. Over two years the gap between compound interest and simple interest is the interest earned in the second year on the first year's interest, and nothing else. That comes to P(r/100)², so 250 = P × (5/100)² = P × 0.0025, which gives P = ₹1,00,000. Checking directly: simple interest is 2 × 5 per cent of 1,00,000 = ₹10,000, while compound interest is 1,00,000 × (1.05² − 1) = 1,00,000 × 0.1025 = ₹10,250. The difference is ₹250, as stated.
- (b)₹80,000 — 80,000 × 0.0025 = ₹200. The gap falls short of the ₹250 the question fixes.
- (c)₹40,000 — 40,000 × 0.0025 = ₹100, less than half the required difference.
- (d)₹1,20,000 — 1,20,000 × 0.0025 = ₹300, which overshoots. The four options are spread on either side of the answer precisely so that a candidate who has the formula can test them in seconds.
Simple interest pays on the principal alone; compound interest pays on the principal and on interest already credited. In the first year the two are identical. From the second year the compound scheme earns interest on the first year's interest, and that single extra term is the whole difference over two years — hence P(r/100)². For three years the difference is P(r/100)²(3 + r/100), which is worth carrying separately.
This is a formula-recall item, and the reverse check is the safety net: multiply each option by 0.0025 and see which gives 250. It takes less time than deriving the answer. The trap for anyone who does not know the shortcut is to compute both interest figures in full and slip somewhere in 1.05², which is 1.1025 and not 1.10.
- For two years, compound interest minus simple interest = P(r/100)².
- For three years the same difference is P(r/100)²(3 + r/100).
- At 5 per cent the two-year factor is 0.0025, so every ₹1,00,000 of principal opens a ₹250 gap.
- 1.05² = 1.1025, so the two-year compound interest rate is 10.25 per cent against a simple 10 per cent.
- The difference arises entirely from interest earned on the first year's interest.
The gap is the second year's interest on the first year's interest — 5 per cent of ₹5,000.
- Using 1.10 instead of 1.1025 for the two-year compound factor.
- Applying the two-year difference formula to a three-year period.
A single-formula item where the four options are spaced so that testing them backwards is faster than solving forwards.
The difference between the simple interest received from two banks on Rs. 500 for two years is Rs. 2·50. What is the difference between their rates?
- (a) 0·25%
- (b) 0·5%
- (c) 1%
- (d) 2·5%
Answer(a) 0·25%
A difference of interests solved by the same move — write the gap as a single expression in the unknown instead of computing both interests and subtracting.
A sum triples in ten years under compound interest at a certain rate of interest, the interest is being compounded annually. In how many years, it would become nine times?
- (a) 20 years
- (b) 30 years
- (c) 40 years
- (d) 50 years
Answer(a) 20 years
The multiplicative nature of compounding seen from the growth side. Because each period multiplies by the same factor, tripling twice takes twice as long — the same reason the second year's interest here is charged on the first year's interest.
- practice — not a real PYQ
The difference between compound and simple interest on a sum for 2 years at 10% per annum is ₹50. The sum is
- (a)₹2,500
- (b)₹5,000
- (c)₹10,000
- (d)₹500
Answer(b) ₹5,000 — P × (10/100)² = 50 gives P × 0.01 = 50.
- practice — not a real PYQ
On ₹8,000 at 5% per annum, by how much does two years of compound interest exceed two years of simple interest?
- (a)₹10
- (b)₹20
- (c)₹40
- (d)₹80
Answer(b) ₹20 — 8,000 × 0.0025 = 20, that is 5 per cent of the first year's ₹400 of interest.