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Rodney has invested ₹15,000 at a rate of 8% p.a. for 1 year on compound interest, compounded half-yearly. The amount received by him will be:
₹16,224
₹15,840
₹16,354
₹15,960
₹16,224
Since the rate is 8% p.a. for 1 year, half-yearly rate is 4% for 2 periods. The effective interest for 2 periods is 4% + 4% + (4% of 4%) = 8.16%. Multiply 15000 by 1.0816 to get 16224.
Principal P = ₹15,000, Annual Rate r = 8%, Time t = 1 year, compounding is half-yearly.
A=P(1+100r/2)2t
Since the rate is 8% p.a. for 1 year, half-yearly rate is 4% for 2 periods. The effective interest for 2 periods is 4% + 4% + (4% of 4%) = 8.16%. Multiply 15000 by 1.0816 to get 16224.
Students often use the full 8% rate or forget to double the number of periods (time) when compounding half-yearly, leading to simple interest calculations.
Identify given variables
Principal P=15000, Rate R=8%, Time T=1 year, and frequency is half-yearly (n=2 periods per year).
P=15000,R=4%,n=2
Apply Compound Interest formula
For compounding half-yearly, we use n=2 half-years, so R becomes R/2=4% and periods become 2T=2.
A=15000(1+1004)2
Calculate the amount
Solve the power: A=15000×(1.04)2=15000×1.0816.
A=15000×1.0816=16224
A is correct because the principal amount of ₹15,000 compounded at 4% for 2 half-yearly periods results in a total amount of ₹16,224.
This concept is foundational for understanding EMI calculations and inflation growth in economics/banking.
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