Meenal lends रु 75,000 at C.I. for 3 years. If the rate of interest for the first two years is 15% per year and for the third year it is 16%, calculate the sum Meenal will get at the end of the third year.

Explanation

To solve the problem of calculating the total amount Meenal will receive at the end of the third year after lending रु 75,000 at compound interest, we will break it down step by step.

### Step 1: Calculate the compound interest for the first year.
- **Principal (P)** = रु 75,000
- **Rate of Interest (R)** = 15% per annum
- **Time (T)** = 1 year

Using the formula for compound interest for the first year:
\[ \text{Compound Interest (CI)} = P \times \frac{R}{100} \times T \]
\[ \text{CI for 1st year} = 75,000 \times \frac{15}{100} \times 1 = 75,000 \times 0.15 = 11,250 \]

### Step 2: Calculate the total amount at the end of the first year.
\[ \text{Amount after 1st year} = P + \text{CI for 1st year} \]
\[ \text{Amount after 1st year} = 75,000 + 11,250 = 86,250 \]

### Step 3: Calculate the compound interest for the second year.
- **New Principal (P)** = Amount after 1st year = रु 86,250
- **Rate of Interest (R)** = 15% per annum
- **Time (T)** = 1 year

Using the formula for compound interest for the second year:
\[ \text{CI for 2nd year} = 86,250 \times \frac{15}{100} \times 1 = 86,250 \times 0.15 = 12,937.50 \]

### Step 4: Calculate the total amount at the end of the second year.
\[ \text{Amount after 2nd year} = \text{Amount after 1st year} + \text{CI for 2nd year} \]
\[ \text{Amount after 2nd year} = 86,250 + 12,937.50 = 99,187.50 \]

### Step 5: Calculate the compound interest for the third year.
- **New Principal (P)** = Amount after 2nd year = रु 99,187.50
- **Rate of Interest (R)** = 16% per annum
- **Time (T)** = 1 year

Using the formula for compound interest for the third year:
\[ \text{CI for 3rd year} = 99,187.50 \times \frac{16}{100} \times 1 = 99,187.50 \times 0.16 = 15,870 \]

### Step 6: Calculate the total amount at the end of the third year.
\[ \text{Total Amount after 3 years} = \text{Amount after 2nd year} + \text{CI for 3rd year} \]
\[ \text{Total Amount after 3 years} = 99,187.50 + 15,870 = 115,057.50 \]

Thus, the total amount Meenal will receive at the end of the third year is **रु 115,057.50**.

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