Single correct option
A sum of ₹10,000 is invested at 20% per annum compounded half-yearly. What is the compound interest earned at the end of 1 year?
- A. ₹2,000
- B. ₹2,100
- C. ₹2,200
- D. ₹2,400
Show answer and solution
Answer: (B) ₹2,100
Compounded half-yearly at 20% per annum means the rate per half-year is 10%, applied over 2 periods (1 year).
Amount = 10000 × (1.10)² = 10000 × 1.21 = ₹12,100.
Compound interest = 12,100 − 10,000 = ₹2,100.
Why others fail: ₹2,000 is the simple interest at 20% for 1 year (ignoring the compounding); ₹2,200 and ₹2,400 come from applying 10% or 20% only once more without squaring correctly.
Tip: With half-yearly compounding, halve the annual rate and double the number of periods before applying the compound interest formula.
Amount = 10000 × (1.10)² = 10000 × 1.21 = ₹12,100.
Compound interest = 12,100 − 10,000 = ₹2,100.
Why others fail: ₹2,000 is the simple interest at 20% for 1 year (ignoring the compounding); ₹2,200 and ₹2,400 come from applying 10% or 20% only once more without squaring correctly.
Tip: With half-yearly compounding, halve the annual rate and double the number of periods before applying the compound interest formula.
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