Kiran's table for a loan of ₹ 25,000 is filled for Year 1 only. Interest is compounded annually at the same rate. What is the total compound interest for the 2 years?
Class 8Comparing QuantitiesComparing Quantities
A₹ 4,160
B₹ 4,000
C₹ 2,160
D₹ 29,160
Step-by-Step Solution
Year 1 interest ₹ 2,000 on ₹ 25,000 means the rate is 8%. Year 2 principal =₹27000, interest =8% of 27000=₹2160. Total CI =2000+2160=₹4160. (₹ 4,000 is simple interest; ₹ 29,160 is the amount.)
Answer: A) ₹ 4,160
Key idea: Compound interest — interest on interest
After year 1, interest is added to principal — so year 2's interest is calculated on a LARGER amount, not the original.
**A=P×(1+R/100)T**, where A is the final amount after T years. **CI = A−P** (the total interest earned).
Example: ₹2000 at 5% for 3 years, compounded annually: - Year 1: 2000×1.05=2100− Year 2: 2100×1.05=2205− Year 3: 2205×1.05=2315.25
Direct formula: A=2000×(1.05)3=2315.25. CI = 2315.25 − 2000 = 315.25 (vs SI of 300 — compound gives more).
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