Ravi deposited Rs 15000 in a scheme which offers compound interest at the rate of 15% per annum for 2 yrs. If due to some emergency, he withdrew 10000 rs at the end of `1^(st)` yr. What amount will ravi get at the end of 2nd year?

Options

A. Rs 8337.5
B. Rs 8625
C. Rs 8725.5
D. Rs 9245.5

Answer

To solve the problem step by step, we will calculate the compound interest for the first year, the amount after the first year, the remaining amount after withdrawal, and finally the amount at the end of the second year.

### Step 1: Calculate the amount after the first year
Ravi deposited Rs. 15,000 at a compound interest rate of 15% per annum for 1 year.

**Formula for Amount (A) after 1 year:**
\[ A = P \times \left(1 + \frac{r}{100}\right)^n \]
Where:
- \( P = 15,000 \) (Principal)
- \( r = 15 \) (Rate of interest)
- \( n = 1 \) (Number of years)

**Calculation:**
\[ A = 15000 \times \left(1 + \frac{15}{100}\right)^1 \]
\[ A = 15000 \times \left(1 + 0.15\right) \]
\[ A = 15000 \times 1.15 \]
\[ A = 15000 \times 1.15 = 17250 \]

### Step 2: Withdraw Rs. 10,000 at the end of the first year
After 1 year, Ravi withdraws Rs. 10,000 from the amount he has.

**Remaining Amount:**
\[ \text{Remaining Amount} = 17250 - 10000 = 7250 \]

### Step 3: Calculate the amount at the end of the second year
Now, the remaining amount of Rs. 7,250 will earn interest for another year at the same rate of 15%.

**Formula for Amount (A) after 1 year:**
\[ A = P \times \left(1 + \frac{r}{100}\right)^n \]
Where:
- \( P = 7250 \) (New Principal after withdrawal)
- \( r = 15 \) (Rate of interest)
- \( n = 1 \) (Number of years)

**Calculation:**
\[ A = 7250 \times \left(1 + \frac{15}{100}\right)^1 \]
\[ A = 7250 \times \left(1 + 0.15\right) \]
\[ A = 7250 \times 1.15 \]
\[ A = 7250 \times 1.15 = 8337.5 \]

### Final Amount at the end of the second year
The total amount Ravi will get at the end of the second year is Rs. 8,337.5.

### Summary
- Amount after 1 year: Rs. 17,250
- Amount after withdrawal: Rs. 7,250
- Amount at the end of 2nd year: Rs. 8,337.5

### Conclusion
Ravi will receive Rs. 8,337.5 at the end of the second year.

---