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Compound Interest: Half-Yearly and Quarterly Compounding Questions with Solutions

The compound interest formula doesn’t change when compounding happens more often than once a year — only the rate and the time do, and getting that adjustment right is the entire skill in this topic. Here’s the concept, four fully worked examples, and a few to try yourself.

The concept, quickly

  • For half-yearly compounding: divide the annual rate by 2, and multiply the time (in years) by 2, before applying Amount = P × (1 + rate/100)^periods.
  • For quarterly compounding: divide the annual rate by 4, and multiply the time (in years) by 4.
  • The underlying formula never changes — only what counts as "the rate per period" and "the number of periods" does. Get those two numbers right first, then it’s the same calculation as annual compounding.
  • Compound Interest = Amount − Principal, exactly as with annual compounding — this last step is easy to forget after focusing on the rate/time adjustment.

Worked examples

1. Find the compound interest on ₹10,000 for 1 year at 10% per annum, compounded half-yearly.

Solution

  1. Half-yearly: rate per period = 10/2 = 5%, number of periods = 1 × 2 = 2.
  2. Amount = 10,000 × (1.05)² = 10,000 × 1.1025 = ₹11,025.
  3. Compound Interest = 11,025 − 10,000 = ₹1,025.

Answer: ₹1,025

2. Find the amount on ₹10,000 for 6 months at 8% per annum, compounded quarterly.

Solution

  1. Quarterly: rate per period = 8/4 = 2%. 6 months = 1/2 year, so number of periods = (1/2) × 4 = 2.
  2. Amount = 10,000 × (1.02)² = 10,000 × 1.0404 = ₹10,404.

Answer: ₹10,404

3. Find the compound interest on ₹20,000 for 1 year at 20% per annum, compounded half-yearly.

Solution

  1. Half-yearly: rate per period = 20/2 = 10%, number of periods = 1 × 2 = 2.
  2. Amount = 20,000 × (1.10)² = 20,000 × 1.21 = ₹24,200.
  3. Compound Interest = 24,200 − 20,000 = ₹4,200.

Answer: ₹4,200

4. Find the compound interest on ₹15,000 for 1.5 years at 20% per annum, compounded half-yearly.

Solution

  1. Half-yearly: rate per period = 20/2 = 10%. 1.5 years means number of periods = 1.5 × 2 = 3.
  2. Amount = 15,000 × (1.10)³ = 15,000 × 1.331 = ₹19,965.
  3. Compound Interest = 19,965 − 15,000 = ₹4,965.

Answer: ₹4,965

Try these yourself

Work out the rate per period and number of periods first, then check against the answer.

1. Find the compound interest on ₹12,000 for 1 year at 10% per annum, compounded half-yearly.

Answer: ₹1,230

2. Find the amount on ₹20,000 for 6 months at 8% per annum, compounded quarterly.

Answer: ₹20,808

3. Find the compound interest on ₹8,000 for 1.5 years at 20% per annum, compounded half-yearly.

Answer: ₹2,648

Where this comes up

Compound Interest with half-yearly or quarterly compounding is a regular sub-topic within the Quantitative/Numerical Aptitude section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk.

Practice more Compound Interest questions

This page covers the concept and a handful of worked examples. Pariksha Saathi has full topic-wise practice sets for Compound Interest (and every other Quant/Reasoning/English topic) with instant scoring and explanations — free, no account required.

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