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Rahul deposits 20,000 in an account that pays 10% annual interest compounded half-yearly. Calculate the total amount after one year.
21,050
22,050
23,050
24,050
22,050
For half-yearly, halve the rate to 5% and double the periods to 2. Calculate two successive increases of 5%: 20,000+5%=21,000, and 21,000+5%=22,050.
Principal P = 20,000, Annual Interest Rate R = 10%, Time T = 1 year, compounding is half-yearly.
A=P(1+100R/nтАЛ)nt
For half-yearly, halve the rate to 5% and double the periods to 2. Calculate two successive increases of 5%: 20,000+5%=21,000, and 21,000+5%=22,050.
Students often fail to halve the annual rate (10%) and double the time (1 year) when the compounding is half-yearly, leading to calculation errors.
Identify parameters
Since interest is compounded half-yearly, the rate R becomes R/2=10%/2=5% per half-year, and the number of periods n becomes 1├Ч2=2 half-years.
RhalfтАЛ=5%,n=2
Apply Compound Interest formula
Substitute the values into the formula A=P(1+r/100)n where r=5 and n=2.
A=20000(1+1005тАЛ)2
Final calculation
Simplify the expression: 20000├Ч(1.05)2=20000├Ч1.1025=22050.
A=20000├Ч1.1025=22050
B is correct because the total amount after two half-yearly periods at a rate of 5% is 22,050.
This concept of adjusting the rate and time for compounding frequency is identical to how you calculate depreciation or population growth shifts over sub-yearly intervals.