The simple interest on a sum of ₹ 8,000 at a certain rate percent per annum for 3 years is ₹ 3,600. If the interest is compounded 8-monthly on the same sum at the same interest rate, then total compound interest after 2 years will be
- (1)₹ 10,248
- (2)₹ 10,648
- (3)₹ 2,248
- (4)₹ 2,648
Answer
Why
Correct — option (4), ₹ 2,648.
Step 1 — find the annual rate from simple interest, SI = P × R × T ÷ 100.
3,600 = 8,000 × R × 3 ÷ 100
3,600 = 240 × R
R = 3,600 ÷ 240 = 15% per annum
Step 2 — convert to the 8-month compounding period.
Rate per period = 15% × 8/12 = 10%
Number of periods = 24 months ÷ 8 = 3
Step 3 — compound for 3 periods.
(1.10)³ = 1.10 × 1.10 × 1.10 = 1.331
Amount = 8,000 × 1.331 = ₹ 10,648
Step 4 — subtract the principal.
Compound interest = 10,648 − 8,000 = ₹ 2,648
Check period by period: 8,000 → 8,800 → 9,680 → 10,648. The interest is 800 + 880 + 968 = ₹ 2,648.
The idea to remember: for compounding every k months, the rate per period is the annual rate × k/12 and the number of periods is the total months ÷ k.
Why the others are wrong
- (1)₹ 10,248 — ₹ 10,248 is larger than the ₹ 8,000 principal itself, far above the ₹ 2,400 simple interest for the same 2 years, so it cannot be interest. It equals ₹ 8,000 plus option (3)'s ₹ 2,248, an amount built on a wrong interest figure.
The stem asks for compound interest alone, which is ₹ 2,648; the amount after 2 years is ₹ 10,648.
- (2)₹ 10,648 — ₹ 10,648 is the amount after 2 years: principal plus interest, 8,000 × 1.331.
The stem asks for the total compound interest, so the principal must be taken away: 10,648 − 8,000 = ₹ 2,648.
- (3)₹ 2,248 — ₹ 2,248 fails a quick check. Simple interest at the same 15% for 2 years is 8,000 × 15 × 2 ÷ 100 = ₹ 2,400.
Compounded over three periods, interest earns interest, so the compound interest must be more than ₹ 2,400. ₹ 2,248 is less, so it cannot be right; the working gives ₹ 2,648.
Concept
Simple interest is charged on the original principal only: SI = P × R × T ÷ 100. Compound interest adds each period's interest to the principal, so later periods earn interest on it.
The compound amount is A = P × (1 + r/100)ⁿ, where r is the rate per period and n the number of periods. Compound interest = A − P.
An annual rate R compounded every k months gives r = R × k/12 per period, with n = total months ÷ k. At 15% a year, 8-month periods carry 10% each.
For the same nominal rate, more frequent compounding gives a larger amount.
RPSC's 2024 syllabus for Reasoning & Mental Ability lists "Simple and Compound Interest" under Basic Numeracy.
The two methods describe how deposits and loans grow. Simple interest grows by the same amount each period; compound interest grows by the same percentage each period, which is geometric growth.
The compound formula is the same one used for population growth at a fixed percentage and, with a minus sign, for depreciation of an asset's value.
Key facts
- Simple interest = P × R × T ÷ 100; here 3,600 = 8,000 × R × 3 ÷ 100 gives R = 15% per annum.
- Compounding every k months: rate per period = annual rate × k/12; number of periods = total months ÷ k.
- Compound amount = P × (1 + r/100)ⁿ with r per period; compound interest = amount − principal.
- (1.1)² = 1.21 and (1.1)³ = 1.331, so 10% over 3 periods multiplies a sum by 1.331.
- Over 3 periods at r% per period, CI − SI = P × (r/100)² × (3 + r/100); here 8,000 × 0.01 × 3.1 = ₹ 248.
Simple interest at 15% a year for 2 years would be ₹ 2,400; the extra ₹ 248 is interest earned on earlier interest.
Study next
Common traps
- Using 15% per period. The 15% is per annum, so an 8-month period carries 15 × 8/12 = 10%; 15% over three periods would give ₹ 4,167 interest.
- Counting two periods because the time is 2 years. At 8 months per period, 24 months hold 3 periods; 15% for two periods would give ₹ 10,580 as the amount.
- Stopping at the amount, ₹ 10,648, when the stem asks for the total compound interest.
A question can give simple interest and ask for compound interest at the same rate, or give the difference between the two and ask for the principal or the rate.
A question can set the compounding period at a year, half a year, a quarter, or an interval such as 8 months.
Related PYQs
UnlockIAS will link similar questions from RAS Pre 2023 and 2016 here once those papers are published on this site.
Practice
- practice — not a real PYQ
The simple interest on ₹ 10,000 for 2 years is ₹ 2,400. What is the compound interest on the same sum for 1 year at the same annual rate, if interest is compounded every 6 months?
- (a)₹ 1,200
- (b)₹ 1,236
- (c)₹ 11,236
- (d)₹ 2,544
Answer(2) — Rate = 12% a year, so 6% per half-year for 2 periods: 10,000 × 1.1236 = ₹ 11,236, and interest = ₹ 1,236.Option (1) is simple interest for 1 year; option (3) is the amount; option (4) is compound interest at 12% a year for 2 years.
- practice — not a real PYQ
What is the compound interest on ₹ 16,000 for 9 months at 20% per annum, compounded quarterly?
- (a)₹ 2,400
- (b)₹ 2,522
- (c)₹ 18,522
- (d)₹ 11,648
Answer(2) — 5% per quarter for 3 quarters: 16,000 × 1.157625 = ₹ 18,522, so interest = ₹ 2,522.Option (1) is simple interest for 9 months; option (3) is the amount; option (4) applies 20% to each quarter.