A sum of rupes 1,536 , put at compund interest amounts to rupes 1,632 in one years How much would it amount to in the second year?

Answer

To solve the problem step by step, we will use the formula for compound interest and calculate the amount for the second year.

### Step 1: Identify the given values
- Principal (P) = ₹1,536
- Amount after 1 year (A) = ₹1,632

### Step 2: Calculate the interest earned in the first year
To find the interest earned in the first year, we subtract the principal from the amount after one year:

\[ \text{Interest for 1st year} = A - P = 1632 - 1536 = ₹96 \]

### Step 3: Calculate the rate of interest (r)
We can use the formula for compound interest to find the rate of interest. The formula is:

\[ A = P \left(1 + \frac{r}{100}\right)^n \]

For n = 1 year:

\[ 1632 = 1536 \left(1 + \frac{r}{100}\right)^1 \]

Dividing both sides by 1536:

\[ \frac{1632}{1536} = 1 + \frac{r}{100} \]

Calculating the left side:

\[ \frac{1632}{1536} = 1.0625 \]

So we have:

\[ 1.0625 = 1 + \frac{r}{100} \]

Subtracting 1 from both sides:

\[ 0.0625 = \frac{r}{100} \]

Multiplying both sides by 100:

\[ r = 6.25\% \]

### Step 4: Calculate the amount after the second year
Now we can find the amount after the second year using the same formula:

\[ A = P \left(1 + \frac{r}{100}\right)^n \]

For n = 2 years:

\[ A = 1536 \left(1 + \frac{6.25}{100}\right)^2 \]

Calculating \(1 + \frac{6.25}{100}\):

\[ 1 + 0.0625 = 1.0625 \]

Now squaring it for 2 years:

\[ (1.0625)^2 = 1.12890625 \]

Now, substituting back into the formula:

\[ A = 1536 \times 1.12890625 \]

Calculating this gives:

\[ A \approx 1734 \]

### Final Answer
The amount after the second year would be approximately ₹1,734.

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