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# Neelkanth invested 45000 for 3 years at compound interest which is compounded annually. if the rate of interest is 5% p.a. for the first year, 10% p.a. for the second year and 20% p.a. for the third year, how much interest will he earn after three years?

To calculate the compound interest earned by Neelkanth after three years with varying interest rates, we can follow these steps:

1. Calculate the amount after the first year (5% interest rate).
2. Calculate the amount after the second year (10% interest rate).
3. Calculate the amount after the third year (20% interest rate).
4. Calculate the total interest earned.

Let’s go through these steps:

1. Calculate the amount after the first year (5% interest rate):

Amount_After_1st_Year = Principal × (1 + Interest_Rate_1st_Year) Amount_After_1st_Year = 45,000 × (1 + 0.05) Amount_After_1st_Year = 45,000 × 1.05 Amount_After_1st_Year = Rs 47,250

1. Calculate the amount after the second year (10% interest rate):

Amount_After_2nd_Year = Amount_After_1st_Year × (1 + Interest_Rate_2nd_Year) Amount_After_2nd_Year = 47,250 × (1 + 0.10) Amount_After_2nd_Year = 47,250 × 1.10 Amount_After_2nd_Year = Rs 51,975

1. Calculate the amount after the third year (20% interest rate):

Amount_After_3rd_Year = Amount_After_2nd_Year × (1 + Interest_Rate_3rd_Year) Amount_After_3rd_Year = 51,975 × (1 + 0.20) Amount_After_3rd_Year = 51,975 × 1.20 Amount_After_3rd_Year = Rs 62,370

1. Calculate the total interest earned:

Total_Interest_Earned = Amount_After_3rd_Year – Principal Total_Interest_Earned = 62,370 – 45,000 Total_Interest_Earned = Rs 17,370

So, Neelkanth will earn a total interest of Rs 17,370 after three years with the given varying interest rates.

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