Question : Rs. 30,000 is lent at compound interest (compounded annually) for 3 years. If the rate of interest is 10% for the first year, 20% for the second year, and 30% for the third year, then what will be the total compound interest?
Option 1: Rs. 21,480
Option 2: Rs. 19,270
Option 3: Rs. 20,560
Option 4: Rs. 22,580
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Correct Answer: Rs. 21,480
Solution : Given: Rs. 30,000 is lent at compound interest (compounded annually) for 3 years. The interest rate is 10% for the first year, 20% for the second year, and 30% for the third year. We know, $\text{Total Amount}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$ The amount after 1 year $=30000[1+\frac{10}{100}]^1$ $=30000\times[1+0.1]=30000\times 1.1 =$ Rs. 33,000 The amount after 2 years $=33000[1+\frac{20}{100}]^1$ $=33000\times[1+0.2]=33000\times 1.2 =$ Rs. 39,600 The amount after 3 years $=39600[1+\frac{30}{100}]^1$ $=39600\times[1+0.3]=39600\times 1.3 =$ Rs. 51,480 The total compound interest = 51,480 – 30,000 = Rs. 21,480 Hence, the correct answer is Rs. 21,480.
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