ABHYAS PREP: COMMERCIAL ARITHMETIC · SIMPLE & COMPOUND INTEREST

Compound interest compounded half-yearly

Half-yearly compounding: halve the rate and double the number of periods, then use A = P(1 + r/100)^n.

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Worked examples

Example 1 · level 1

Find the compound interest on ₹6,000 at 20% per annum for 1 year, interest compounded half-yearly.

₹1,200
₹1,260
₹1,285
₹7,260

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Rate per half-year = 20/2 = 10%; periods = 2.
Amount = ₹6,000 × 1.1^2 = ₹7,260.
CI = ₹7,260 − ₹6,000 = ₹1,260.

Answer: ₹1,260

Example 2 · level 2

Find the compound interest on ₹19,000 at 10% per annum for 1.5 years, interest compounded half-yearly.

₹2,850
₹2,920.1
₹2,994.88
₹21,994.88

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Rate per half-year = 10/2 = 5%; periods = 3.
Amount = ₹19,000 × 1.05^3 = ₹21,994.88.
CI = ₹21,994.88 − ₹19,000 = ₹2,994.88.

Answer: ₹2,994.88

Example 3 · level 3

Find the compound interest on ₹9,000 at 8% per annum for 1.5 years, interest compounded half-yearly.

₹1,080
₹1,101.32
₹1,123.78
₹10,123.78

Show solution

Rate per half-year = 8/2 = 4%; periods = 3.
Amount = ₹9,000 × 1.04^3 = ₹10,123.78.
CI = ₹10,123.78 − ₹9,000 = ₹1,123.78.

Answer: ₹1,123.78