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Find the compound interest on ₹11,000 in 2 years at 4% p.a., interest compounded yearly.
₹875.80
₹906.50
₹786.60
₹897.60
₹897.60
Use successive percentage change for 2 years: 4% + 4% +1004×4 = 8.16%. Then CI = 8.16% of 11,000=897.60.
Principal (P) = ₹11,000, Time (n) = 2 years, Rate of Interest (R) = 4% p.a., compounded yearly.
A=P(1+100R)n, and Compound Interest (CI)=A−P
Use successive percentage change for 2 years: 4% + 4% +1004×4 = 8.16%. Then CI = 8.16% of 11,000=897.60.
Students often calculate Simple Interest instead of Compound Interest, resulting in 11,000 ×0.04×2=880.
Identify Given Parameters
We are given the principal amount P=₹11,000, time period n=2 years, and annual interest rate R=4%.
P=11000,R=4% p.a.,n=2 years
Apply Compound Amount Formula
Substitute the values into the compound amount formula A=P(1+100R)n.
A=11000(1+1004)2=11000×(1.04)2
Calculate Total Amount
Compute (1.04)2=1.0816 and multiply by 11,000 to find the total amount A.
A=11000×1.0816=11897.60
Calculate Compound Interest
Subtract the principal P from the total amount A to find the compound interest.
CI=A−P=11897.60−11000=897.60
D is correct because the compound interest calculated on ₹11,000 for 2 years at 4% p.a. is ₹897.60.
For 2 years, the effective compound interest rate percentage can also be calculated using the successive formula x+y+100xy, which gives 4+4+10016=8.16%. Directly taking 8.16% of ₹11,000 yields ₹897.60 instantly.
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