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Find the compound interest on ₹12,000 at 10% per annum for 1.5 years, if the interest is compounded half-yearly.
₹1,891.50
₹1,920.00
₹1,860.00
₹1,950.50
₹1,891.50
Compound interest calculated half-yearly splits the annual rate into half and doubles the number of compounding periods. For ₹12,000 at 10% per annum for 1.5 years compounded half-yearly, the rate becomes 5% per half-year and time becomes 3 half-years, resulting in an amount of ₹13,891.50 and a compound interest of ₹1,891.50.
Compound interest calculated half-yearly splits the annual rate into half and doubles the number of compounding periods. For ₹12,000 at 10% per annum for 1.5 years compounded half-yearly, the rate becomes 5% per half-year and time becomes 3 half-years, resulting in an amount of ₹13,891.50 and a compound interest of ₹1,891.50.
Think of earning interest every six months like a bank resetting your savings account with fresh bonus interest twice a year, which then starts earning its own interest faster than yearly compounding.
A=P(1+200R)2t — Total amount under half-yearly compounding
CI=A−P — Compound interest formula
The formula for the amount under half-yearly compounding is A=P(1+200R)2t, where P is the principal, R is the annual interest rate, and t is time in years. Substituting the given values gives 12000×(1+1005)3, which yields the total amount. Subtracting the principal from this amount gives the compound interest.
When interest is compounded half-yearly, the rate of interest is halved and the time period is doubled.
Compound interest yields higher returns than simple interest due to compounding on previously earned interest.
Provides higher returns on investments compared to simple interest.
Results in higher interest liabilities when applied to loans.
Bank fixed deposits
Loan amortizations
Standard compounding frequency for half-yearly is twice a year.
Option B, C, and D represent incorrect calculations or simple interest values.
A is correct — the compound interest calculated half-yearly for 1.5 years at 10% per annum on ₹12,000 is ₹1,891.50.
Always check the compounding frequency carefully in quantitative problems; half-yearly means dividing the rate by 2 and multiplying time by 2.
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