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What is the compound interest on ₹10,000 at 10% per annum for 2 years compounded half-yearly?
₹2155
₹2255
₹2355
₹2455
₹2155
The compound interest on ₹10,000 at 10% per annum compounded half-yearly for 2 years is calculated using the amount formula A=P(1+100R)n, yielding an amount of ₹12,155 and a compound interest of ₹2155.
The compound interest on ₹10,000 at 10% per annum compounded half-yearly for 2 years is calculated using the amount formula A=P(1+100R)n, yielding an amount of ₹12,155 and a compound interest of ₹2155.
Think of compound interest like a snowball rolling down a hill; every six months, the snow collected so far gets its own new layer of snow, compounding the growth faster than simple interest.
A=P(1+100r)n — Total amount formula for compound interest
CI=A−P — Compound interest formula
When interest is compounded half-yearly, the annual rate is divided by 2 (becoming 5% per half-year) and the time period in years is multiplied by 2 (becoming 4 half-year periods). The total amount is computed as A=10000×(1+1005)4, and subtracting the principal gives the compound interest.
Principal amount (P) = ₹10,000
Nominal annual rate = 10%, so half-yearly rate (r) = 5%
Time period = 2 years, so number of half-yearly periods (n) = 2×2=4
Provides higher returns on investments compared to simple interest over time
Increases liability rapidly for loans and borrowings if not paid promptly
Bank fixed deposits and savings accounts
Loans, mortgages, and financial planning
Option B (₹2255) represents an incorrect calculation or confusion with annual compounding.
Exact calculated value: 10000×(1.05)4−10000=10000×1.21550625−10000=2155.06
A is correct — The calculated compound interest is ₹2155.
Always adjust the rate and time period properly when compounding frequency is other than annual (e.g., half-yearly, quarterly).
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