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What will be the amount after 1 year if a sum of ₹7,500 is invested at 8% compound interest per annum, compounded half-yearly?
₹8,300
₹8,112
₹8,220
₹8,140
₹8,112
Since the interest is compounded half-yearly, calculate for two periods (6 months each) at 4% (half of 8%) per period. First 6 months: 4% of 7500 = 300; Next 6 months: 4% of (7500+300) = 4% of 7800 = 312. Total = 7500 + 300 + 312 = 8112.
Principal P = ₹7,500, Rate R = 8% per annum, Time n = 1 year, Compounded half-yearly
A=P(1+100R/2)2n
Since the interest is compounded half-yearly, calculate for two periods (6 months each) at 4% (half of 8%) per period. First 6 months: 4% of 7500 = 300; Next 6 months: 4% of (7500+300) = 4% of 7800 = 312. Total = 7500 + 300 + 312 = 8112.
Students often forget to halve the rate (8% becomes 4%) and double the time (1 year becomes 2 half-years) for compound interest.
Identify parameters
Since compounding is half-yearly, the rate of interest R is halved and the time n is doubled.
Rate=28%=4%,Time=1×2=2 half-years
Apply Compound Interest Formula
Substitute the values into the formula A=P(1+r/100)n where P=7500, r=4, and n=2.
A=7500(1+1004)2
Calculate the amount
Simplify the expression: A=7500×(1.04)2=7500×1.0816.
A=7500×1.0816=8112
B is correct because the calculated amount after 1 year with half-yearly compounding is ₹8,112.
This concept of compounding frequency is essential for solving problems on bank deposits and inflation in Quantitative Aptitude sections.
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