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Find the compound interest on ₹12,000 in 3 years at a rate of 10% per annum, compounded annually.
₹3,872
₹3,672
₹3,772
₹3,972
₹3,972
Use the ratio 1:3:3:1 or 3:3:1 for compound interest over 3 years: 10% of 12,000 = 1,200; 10% of 1,200 = 120; 10% of 120 = 12. Total CI = 3(1,200) + 3(120) + 1(12) = 3,600 + 360 + 12 = 3,972.
Principal P = ₹12,000, Time t = 3 years, Rate r = 10% per annum
CI=P(1+100r)n−P
Use the ratio 1:3:3:1 or 3:3:1 for compound interest over 3 years: 10% of 12,000 = 1,200; 10% of 1,200 = 120; 10% of 120 = 12. Total CI = 3(1,200) + 3(120) + 1(12) = 3,600 + 360 + 12 = 3,972.
Many students calculate simple interest (12,000×0.1×3=3,600) or forget to add the interest on interest, leading to incorrect choices like 3,600 or 3,672.
Identify parameters
The principal amount is P=12000, rate is r=10%, and the time period is n=3 years.
P=12000,r=10%,n=3
Calculate Amount using Compound Interest formula
Use the compound interest formula A=P(1+r/100)n to find the total maturity amount.
A=12000(1+10010)3=12000×(1.1)3
Compute the total amount
Calculate (1.1)3=1.331, then multiply by the principal: 12000×1.331=15972.
A=12000×1.331=15972
Find Compound Interest
Subtract the principal from the total amount to get the interest: CI=A−P=15972−12000=3972.
CI=15972−12000=3972
D is correct because the compound interest on ₹12,000 for 3 years at 10% per annum is ₹3,972.
For shorter time periods like 2 years, use the formula 2r+r2/100 as a percentage of the principal to find the interest directly.
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