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The price of an article is тВ╣2500. It increases by 20% in the first year and by 20% in the second year. What is the price after two years?
3500
3600
3200
3400
3600
Use the successive change formula: x+y+100xyтАЛ. Here, 20+20+10020├Ч20тАЛ=44%. Calculate 44% of 2500 (1100) and add to the original, or simply compute 1.44├Ч2500.
Initial price = 2500, First year increase = 20%, Second year increase = 20%.
Final┬аValue=P├Ч(1+100r1тАЛтАЛ)├Ч(1+100r2тАЛтАЛ)
Use the successive change formula: x+y+100xyтАЛ. Here, 20+20+10020├Ч20тАЛ=44%. Calculate 44% of 2500 (1100) and add to the original, or simply compute 1.44├Ч2500.
Students often add 20% and 20% to get 40%, then calculate 40% of 2500, resulting in 3500, which is incorrect as they ignore the compounding effect on the second year's price.
Calculate the effective percentage increase
To find the combined effect of two successive increases, apply the formula ReffтАЛ=x+y+100xyтАЛ.
20+20+10020├Ч20тАЛ=40+4=44%
Calculate the final price
Apply the 44% increase to the original price of 2500.
Final┬аPrice=2500+(10044тАЛ├Ч2500)=2500+1100=3600
B is correct because the successive 20% increase on 2500 results in a final price of 3600.
This concept is identical to Compound Interest for 2 years. It is also used frequently in Population Growth problems and Depreciation (using negative signs).