Rs. 1000 is being charged at 50% per annum what is the interest for `3^(rd)` year at compound interest ?

Options

A. 1122
B. 1025
C. 1125
D. 625

Answer

To find the interest for the 3rd year at compound interest for Rs. 1000 charged at 50% per annum, we can follow these steps:

### Step 1: Calculate the amount after the first 2 years.
The formula for the amount (A) in compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \( P \) = Principal amount (initial amount)
- \( r \) = Rate of interest per annum
- \( n \) = Number of years

Given:
- \( P = 1000 \)
- \( r = 50\% \)
- \( n = 2 \)

Substituting the values into the formula:
\[ A = 1000 \left(1 + \frac{50}{100}\right)^2 \]
\[ A = 1000 \left(1 + 0.5\right)^2 \]
\[ A = 1000 \left(1.5\right)^2 \]
\[ A = 1000 \times 2.25 \]
\[ A = 2250 \]

### Step 2: Calculate the interest for the 3rd year.
Now, the amount after 2 years (Rs. 2250) will be the principal for the 3rd year. We will use the same formula to find the amount for the 3rd year.

Using:
- \( P = 2250 \)
- \( r = 50\% \)
- \( n = 1 \)

Substituting the values into the formula:
\[ A = 2250 \left(1 + \frac{50}{100}\right)^1 \]
\[ A = 2250 \left(1 + 0.5\right)^1 \]
\[ A = 2250 \times 1.5 \]
\[ A = 3375 \]

### Step 3: Calculate the interest for the 3rd year.
The interest for the 3rd year is the amount after 3 years minus the amount after 2 years:
\[ \text{Interest for 3rd year} = A_{3rd} - A_{2nd} \]
\[ \text{Interest for 3rd year} = 3375 - 2250 \]
\[ \text{Interest for 3rd year} = 1125 \]

Thus, the interest for the 3rd year at compound interest is **Rs. 1125**.

---