A man deposite Rs.500 at the beginning of each year for 2 years at 10% p.a company annually. Find the maturity value at the end of the `2^(nd)` years .
A. Rs .1,050
B.Rs.1,150
C. Rs . 1,155
D.Rs.1,200

Options

A. A
B. D
C. C
D. B

Answer

To find the maturity value of the deposits made by the man, we will calculate the future value of each deposit at the end of 2 years using the formula for compound interest.

### Step-by-Step Solution:

1. **Identify the deposits and interest rate**:
- The man deposits Rs. 500 at the beginning of each year for 2 years.
- The interest rate is 10% per annum.

2. **Calculate the maturity value of the first deposit**:
- The first deposit of Rs. 500 is made at the beginning of the first year. It will earn interest for 2 years.
- Future Value (FV) of the first deposit can be calculated using the formula:
\[ FV = P(1 + r)^n \]
where \( P \) is the principal amount (Rs. 500), \( r \) is the interest rate (10% or 0.10), and \( n \) is the number of years (2).
- Therefore,
\[ FV_1 = 500(1 + 0.10)^2 = 500(1.10)^2 = 500 \times 1.21 = 605 \]

3. **Calculate the maturity value of the second deposit**:
- The second deposit of Rs. 500 is made at the beginning of the second year. It will earn interest for 1 year.
- Using the same formula:
\[ FV_2 = 500(1 + 0.10)^1 = 500(1.10) = 500 \times 1.10 = 550 \]

4. **Calculate the total maturity value**:
- Now, we add the future values of both deposits to find the total maturity value:
\[ Total\ Maturity\ Value = FV_1 + FV_2 = 605 + 550 = 1155 \]

### Final Answer:
The maturity value at the end of the 2nd year is Rs. 1155.