Simple and compound interest for RRB Group D

Interest is the money paid for using someone else's money. A bank pays you interest on a deposit; you pay a lender interest on a loan. In the exam, the question is almost always one of two kinds: simple interest, where the interest is the same every year, and compound interest, where each year's interest is added to the sum and earns interest itself.

Both are percentage questions at heart. If the percentage guide feels comfortable, this topic will too.

Simple interest (SI)

Interest is worked out on the original sum, the principal, every year. It never changes.

• SI = P × R × T ÷ 100
• Amount = P + SI

P = principal, R = rate per cent per year, T = time in years.

The same formula rearranged finds any missing value:

Doubling and tripling at SI: a sum becomes n times itself when the interest equals (n − 1) × P. So R × T = (n − 1) × 100. It doubles when R × T = 100 and triples when R × T = 200.

Compound interest (CI)

Each year's interest is added to the principal, and next year's interest is worked out on the new total.

• Amount = P × (1 + R/100)ᵀ
• CI = Amount − P

For 2 or 3 years, the year-by-year method is quickest and hard to get wrong: find each year's interest on the current amount and add it.

Compounded half-yearly

If interest is added every six months, halve the rate and double the number of periods. 10% a year compounded half-yearly for 1 year is the same as 5% for 2 periods.

SI and CI compared

The CI − SI shortcut

For the same P and R:

• 2 years: CI − SI = P × (R/100)²
• 3 years: CI − SI = P × (R/100)² × (3 + R/100)

The 2-year gap is just interest on the first year's interest.

Worked examples

Example 1: Find the SI on ₹4,000 at 6% for 3 years.

• 4,000 × 6 × 3 ÷ 100 = ₹720.

Example 2: A sum amounts to ₹6,500 in 3 years and ₹7,000 in 4 years at simple interest. Find the sum and the rate.

• One year's interest = 7,000 − 6,500 = 500.
• Three years' interest = 1,500, so P = 6,500 − 1,500 = ₹5,000.
• R = 500 ÷ 5,000 × 100 = 10%.

Example 3: Find the CI on ₹5,000 at 10% for 2 years.

• Year 1: interest 500; amount 5,500.
• Year 2: interest 550; amount 6,050.
• CI = ₹1,050.

Example 4: Find the CI on ₹10,000 at 10% a year, compounded half-yearly, for 1 year.

• Rate 5% per half-year, 2 periods.
• 10,000 → 10,500 → 11,025. CI = ₹1,025.
• Compare: yearly compounding would give only ₹1,000.

Example 5: Find the difference between CI and SI on ₹10,000 at 5% for 2 years.

• 10,000 × (5/100)² = 10,000 × 0.0025 = ₹25.

Example 6: Find the difference between CI and SI on ₹1,000 at 10% for 3 years.

• 1,000 × (10/100)² × (3 + 0.1) = 1,000 × 0.01 × 3.1 = ₹31.
• Check: CI = 1,331 − 1,000 = 331; SI = 300; gap = 31.

Common mistakes

• Using SI when the question says "compound", or the reverse.
• Giving the amount when the question asks for the interest.
• Forgetting to change months or days into years.
• For half-yearly compounding, halving the rate but not doubling the periods.
• Adding the same interest each year in a CI question.

Practice set

1. Find the SI on ₹2,500 at 4% for 2 years.
2. The SI on a sum is ₹600 at 5% for 4 years. Find the sum.
3. Find the SI on ₹1,200 at 5% for 9 months.
4. At what SI rate does a sum triple in 20 years?
5. In how many years will a sum double at 12.5% SI?
6. Find the amount on ₹8,000 at 10% CI for 2 years.
7. Find the CI on ₹4,000 at 5% for 2 years.
8. Find the difference between CI and SI on ₹20,000 at 10% for 2 years.

Answers:

1. ₹200. 2,500 × 4 × 2 ÷ 100.
2. ₹3,000. 600 × 100 ÷ (5 × 4).
3. ₹45. 9 months = 3/4 year; 1,200 × 5 × 3/4 ÷ 100.
4. 10%. Tripling means R × T = 200; 200 ÷ 20.
5. 8 years. R × T = 100; 100 ÷ 12.5.
6. ₹9,680. 8,000 → 8,800 → 9,680.
7. ₹410. 4,000 → 4,200 → 4,410.
8. ₹200. 20,000 × (10/100)².

What to do next

• Learn the SI formula in all four forms and the doubling rule.
• Practise ten CI questions with the year-by-year method before using the formula.
• Memorise the 2-year CI − SI shortcut and check it once by full working.
• Revise profit and loss, then move on to time and work.