Rs. 50000 is borrowed at CI at the rate of 1% for the first year, 2% for the second year and 3% for the third year. Find the amount to be paid after 3 years.

Answer

To solve the problem of finding the amount to be paid after borrowing Rs. 50,000 at compound interest rates of 1% for the first year, 2% for the second year, and 3% for the third year, we can follow these steps:

### Step 1: Calculate the amount after the first year
The principal amount (P) is Rs. 50,000, and the interest rate for the first year (R1) is 1%.

\[ \text{Amount after 1st year} = P + \left(\frac{R1}{100} \times P\right) \]

\[ \text{Amount after 1st year} = 50000 + \left(\frac{1}{100} \times 50000\right) = 50000 + 500 = 50500 \]

### Step 2: Calculate the amount after the second year
Now, we take the amount from the first year as the principal for the second year. The interest rate for the second year (R2) is 2%.

\[ \text{Amount after 2nd year} = \text{Amount after 1st year} + \left(\frac{R2}{100} \times \text{Amount after 1st year}\right) \]

\[ \text{Amount after 2nd year} = 50500 + \left(\frac{2}{100} \times 50500\right) = 50500 + 1010 = 51510 \]

### Step 3: Calculate the amount after the third year
Now, we take the amount from the second year as the principal for the third year. The interest rate for the third year (R3) is 3%.

\[ \text{Amount after 3rd year} = \text{Amount after 2nd year} + \left(\frac{R3}{100} \times \text{Amount after 2nd year}\right) \]

\[ \text{Amount after 3rd year} = 51510 + \left(\frac{3}{100} \times 51510\right) = 51510 + 1545.30 = 53055.30 \]

### Final Amount
The final amount to be paid after 3 years is approximately Rs. 53055.30.

### Summary of Steps:
1. Calculate the amount after the first year using the first year's interest rate.
2. Use the amount from the first year to calculate the amount after the second year with the second year's interest rate.
3. Use the amount from the second year to calculate the amount after the third year with the third year's interest rate.