Saurabh invests रु 48,000 for 7 years at 10% per annum compound interest. Calculate :
(i) the interest for the first year.
(ii) the amount at the end of the second year.
(iii) the interest for the third year.

Explanation

Let's solve the problem step by step.

### Given:
- Principal (P) = रु 48,000
- Rate of interest (R) = 10% per annum
- Time (T) = 7 years

### (i) Calculate the interest for the first year:
To find the interest for the first year, we use the formula for simple interest:

\[ \text{Interest} (I) = \frac{P \times R \times T}{100} \]

Substituting the values for the first year (T = 1):

\[ I = \frac{48000 \times 10 \times 1}{100} \]

Calculating this:

\[ I = \frac{480000}{100} = 4800 \]

So, the interest for the first year is **रु 4,800**.

### (ii) Calculate the amount at the end of the second year:
To find the amount at the end of the second year, we first need to find the amount after the first year and then use that to find the amount after the second year.

The amount after the first year (A1) is given by:

\[ A_1 = P + I_1 \]

Where \(I_1\) is the interest for the first year.

\[ A_1 = 48000 + 4800 = 52800 \]

Now, we calculate the interest for the second year using the new principal (A1):

\[ I_2 = \frac{A_1 \times R \times T}{100} = \frac{52800 \times 10 \times 1}{100} \]

Calculating this:

\[ I_2 = \frac{528000}{100} = 5280 \]

Now, the amount at the end of the second year (A2) is:

\[ A_2 = A_1 + I_2 = 52800 + 5280 = 58080 \]

So, the amount at the end of the second year is **रु 58,080**.

### (iii) Calculate the interest for the third year:
To find the interest for the third year, we will use the amount at the end of the second year as the new principal.

Using the same formula for interest:

\[ I_3 = \frac{A_2 \times R \times T}{100} = \frac{58080 \times 10 \times 1}{100} \]

Calculating this:

\[ I_3 = \frac{580800}{100} = 5808 \]

So, the interest for the third year is **रु 5,808**.

### Summary of Results:
1. Interest for the first year: **रु 4,800**
2. Amount at the end of the second year: **रु 58,080**
3. Interest for the third year: **रु 5,808**

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