To solve this problem, we can use the formula for the future value of an ordinary annuity. Since Mr. X is depositing ₹2000 at the end of each year for 5 years at an annual interest rate of 5% compounded annually, the future value can be calculated as follows:

Future Value of an Ordinary Annuity Formula:

$FV = P \cdot \frac{(1 + r)^n - 1}{r}$ Where:

• $FV$ = Future value (amount of money at the end of 5 years)
• $P$ = Annual deposit = ₹2000
• $r$ = Annual interest rate = $5\% = 0.05$
• $n$ = Number of years = 5

Substituting the values:

$FV = 2000 \cdot \frac{(1 + 0.05)^5 - 1}{0.05}$

1. Compute $(1 + 0.05)^5$: $(1 + 0.05)^5 = 1.2762815625$

2. Subtract 1: $1.2762815625 - 1 = 0.2762815625$

3. Divide by $r = 0.05$: $\frac{0.2762815625}{0.05} = 5.52563125$

4. Multiply by $P = 2000$: $FV = 2000 \cdot 5.52563125 = 11,051.26$

Final Answer:

The amount of money Mr. X will receive at the end of 5 years is ₹11,051.26.

Would you like further clarification or detailed steps for this solution? Let me know!

Here are some related questions for further exploration:

1. How would the result change if the interest rate were 6% instead of 5%?
2. What would be the total interest earned over 5 years?
3. How would the calculation differ if the deposits were made at the beginning of each year?
4. What is the formula for a single lump-sum deposit compounded over time?
5. How does compounding frequency (e.g., quarterly vs annually) affect the future value?

Tip: For similar problems, always verify whether deposits are made at the end or beginning of the period, as it changes the formula slightly!