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Lalit deposits ₹42,000 in his account that pays an annual interest rate of 20% compounded half yearly. Calculate the total amount in his account after one year.
₹50,820
₹50,650
₹50,680
₹50,880
₹50,820
Since the rate is 20% p.a. compounded half-yearly, the effective rate for each 6-month period is 10%. Using the successsive percentage change formula 10+10+10010×10=21%. Thus, 42000×1.21=50820.
Principal P = ₹42,000, Annual Interest Rate R = 20%, Time T = 1 year, Compounding frequency = half-yearly.
A=P(1+100R/2)2n
Since the rate is 20% p.a. compounded half-yearly, the effective rate for each 6-month period is 10%. Using the successsive percentage change formula 10+10+10010×10=21%. Thus, 42000×1.21=50820.
Students often fail to adjust both the rate (dividing by 2) and the time (multiplying by 2) when the interest is compounded half-yearly.
Identify parameters
Convert the annual rate and period to half-yearly intervals. Rate r=20%/2=10% per half-year, and periods n=1 year×2=2 half-years.
r=10%,n=2
Apply Compound Interest formula
Substitute the values into the formula A=P(1+r/100)n.
A=42000(1+10010)2
Calculation
Solve the expression: A=42000×(1.1)2=42000×1.21.
A=42000×1.21=50820
A is correct because the total amount after one year with 20% annual interest compounded half-yearly is calculated as ₹50,820.
This concept of effective rate (Successive Percentage Change) is extremely useful in profit/loss and population growth problems where periodic increases occur.
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