A man lends रु 12,500 at 12% for the first year, at 15% for the second year and at 18% for the third year. If the rates of interest are compounded yearly, find the difference between the C.I. of the first year and the compound interest for the third year

Explanation

To solve the problem of finding the difference between the compound interest (C.I.) of the first year and the compound interest for the third year, we will follow these steps:

### Step 1: Calculate the Compound Interest for the First Year
The formula for compound interest for one year is:
\[ C.I. = P \times r \]
Where:
- \( P \) = Principal amount
- \( r \) = Rate of interest (as a decimal)

For the first year:
- \( P = 12,500 \)
- \( r = 12\% = 0.12 \)

Calculating the C.I. for the first year:
\[ C.I. = 12,500 \times 0.12 = 1,500 \]

### Step 2: Calculate the Amount at the End of the First Year
The amount at the end of the first year is given by:
\[ A = P + C.I. \]
So,
\[ A = 12,500 + 1,500 = 14,000 \]

### Step 3: Calculate the Compound Interest for the Second Year
Using the amount from the first year as the principal for the second year:
- New Principal \( P = 14,000 \)
- Rate for the second year \( r = 15\% = 0.15 \)

Calculating the C.I. for the second year:
\[ C.I. = 14,000 \times 0.15 = 2,100 \]

### Step 4: Calculate the Amount at the End of the Second Year
\[ A = 14,000 + 2,100 = 16,100 \]

### Step 5: Calculate the Compound Interest for the Third Year
Using the amount from the second year as the principal for the third year:
- New Principal \( P = 16,100 \)
- Rate for the third year \( r = 18\% = 0.18 \)

Calculating the C.I. for the third year:
\[ C.I. = 16,100 \times 0.18 = 2,898 \]

### Step 6: Find the Difference Between the C.I. of the First Year and the C.I. for the Third Year
Now we need to find the difference:
\[ \text{Difference} = C.I. \text{ (First Year)} - C.I. \text{ (Third Year)} \]
\[ \text{Difference} = 1,500 - 2,898 = -1,398 \]

### Final Answer
The difference between the C.I. of the first year and the C.I. for the third year is \(-1,398\).

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