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Pradnya invests ₹2,00,000 in the name of her daughter, who is 16 years old, in a scheme that pays compound interest at a rate of 8% per annum, compounded annually. What will be the total amount due to the daughter when she becomes 18 years old?
₹2,51,250
₹2,52,150
₹2,35,850
₹2,33,280
₹2,33,280
Calculate the interest for 2 years using the successive percentage formula: r+r+100r×r=8+8+10064=16.64%. Then 16.64% of 2,00,000 is 33,280, making the total amount 2,00,000+33,280=2,33,280.
Principal amount P = 2,00,000, Interest rate r = 8% per annum, time period n = 18 - 16 = 2 years
A=P(1+100r)n
Calculate the interest for 2 years using the successive percentage formula: r+r+100r×r=8+8+10064=16.64%. Then 16.64% of 2,00,000 is 33,280, making the total amount 2,00,000+33,280=2,33,280.
Students often calculate simple interest (P×R×T/100) instead of compound interest, leading to the incorrect answer 2,32,000.
Identify variables
Principal P = 2,00,000, Rate r = 8%, and time n = 18 - 16 = 2 years.
P=2,00,000,r=8%,n=2
Apply Compound Interest formula
Substitute the values into the compound interest formula to find the total amount A.
A=2,00,000(1+1008)2
Simplify and Calculate
Calculate (1.08)2 which is 1.1664, then multiply by the principal.
A=2,00,000×1.1664=2,33,280
D is correct because the total amount after 2 years at 8% compound interest is 2,33,280.
This is a basic application of compound interest; remember that for 2 years, the multiplier is (1+r/100)2, which can also be solved as 1+2(r/100)+(r/100)2.
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