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Rajveer has invested ₹16,000 at 10% p.a. for 1 year on compound interest, compounded half-yearly. The amount received by him will be:
₹16,354
₹17,830
₹16,542
₹17,640
₹17,640
Since the rate is 10% p.a. half-yearly, calculate 5% interest for two periods. 5% of 16000 is 800. Interest = 800 + 800 + 5% of 800 = 1600 + 40 = 1640. Amount = 16000 + 1640 = 17640.
Principal P = ₹16,000, Rate R = 10% p.a., Time n = 1 year, Compounding is half-yearly.
A=P(1+100R/2)2n
Since the rate is 10% p.a. half-yearly, calculate 5% interest for two periods. 5% of 16000 is 800. Interest = 800 + 800 + 5% of 800 = 1600 + 40 = 1640. Amount = 16000 + 1640 = 17640.
Students often forget to halve the rate (10% to 5%) and double the time periods (1 year to 2 half-years) when moving to half-yearly compounding.
Identify parameters for half-yearly compounding
For compounding half-yearly, the effective rate is R′=210=5% and the number of periods is n′=1×2=2.
R′=5%,n′=2
Apply compound interest formula
The amount A is calculated using the formula A=P(1+100R′)n′.
A=16000(1+1005)2
Calculate the final amount
Simplify the expression: A=16000×(1.05)2=16000×1.1025.
A=16000×1.1025=17640
D is correct because the calculated compound amount for the given investment is ₹17,640.
Always verify if the compounding frequency matches the time period; if compounding is quarterly, divide the rate by 4 and multiply time by 4.
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