As an investment advisor, you have been approached by a client called Vikas for your advice on investment plan. He is currently 40 years old and has Rs.600,000 in the bank. He plans to work for 20 years more and retire at the age of 60. His present salary is Rs.500,000 per year. He expects his salary to increase at the rate of 12% per year until his retirement.

Vikas has decided to invest his bank balance and future savings in a balanced mutual fund scheme that he believes will provide a return of 9 % per year. You agree with his assessment.

 Vikas seeks your help in answering several questions given below. In answering these questions, ignore the tax factor.

(i) Once he retires at the age of 60, he would like to withdraw Rs.800,000 per year for his consumption needs from his investments for the following 15 years (He expects to live upto the age of 75 years). Each annual withdrawal will be made at the beginning of the year. How much should be the value of his investments when Vikas turns 60, to meet this retirement need?

(ii) How much should Vikas save each year for the next 20 years to be able to withdraw Rs.800,000 per year from the beginning of the 21st year ? Assume that the savings will occur at the end of each year.

*


To address Vikas' investment concerns, let's break down the problem into two parts: 

1. **Calculate the required value of investments at age 60 to meet his retirement needs.**
2. **Determine how much Vikas should save annually over the next 20 years to reach that target.**

### Part (i): Required Value of Investments at Age 60

Vikas wants to withdraw Rs.800,000 per year for 15 years, starting at age 60. We need to calculate the present value (at age 60) of these withdrawals, assuming a 9% annual return on investments.

**Withdrawal Series**: Rs.800,000 annually for 15 years, starting at age 60.
  
Since the withdrawals happen at the beginning of each year, we use the formula for the present value of an annuity due:

\[
PV = \text{Withdrawal Amount} \times \frac{1 - (1 + r)^{-n}}{r} \times (1 + r)
\]

Where:
- \( PV \) is the present value at age 60.
- \( r \) is the annual interest rate (9% or 0.09).
- \( n \) is the number of withdrawals (15 years).
- Withdrawal Amount = Rs.800,000.

Substituting the values:

\[
PV = 800,000 \times \frac{1 - (1 + 0.09)^{-15}}{0.09} \times (1 + 0.09)
\]

Let’s calculate this:

\[
PV = 800,000 \times \left(\frac{1 - (1.09)^{-15}}{0.09}\right) \times 1.09
\]

\[
PV = 800,000 \times \left(\frac{1 - 0.275}{0.09}\right) \times 1.09
\]

\[
PV = 800,000 \times \left(\frac{0.725}{0.09}\right) \times 1.09
\]

\[
PV = 800,000 \times 8.056 \times 1.09 \approx 7,021,264.96
\]

Thus, Vikas needs approximately **Rs.7,021,265** at the age of 60 to meet his retirement needs.

### Part (ii): Annual Savings Required

Now, we need to determine how much Vikas should save each year for the next 20 years to accumulate Rs.7,021,265 by the time he is 60.

We'll use the future value of an annuity formula to calculate the required annual savings:

\[
FV = \text{Savings Amount} \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- \( FV \) is the future value (Rs.7,021,265).
- \( r \) is the annual interest rate (9% or 0.09).
- \( n \) is the number of years (20 years).
- Savings Amount = Unknown (this is what we want to find).

Rearranging to solve for the Savings Amount:

\[
\text{Savings Amount} = \frac{FV}{\frac{(1 + r)^n - 1}{r}}
\]

Substituting the known values:

\[
\text{Savings Amount} = \frac{7,021,265}{\frac{(1.09)^{20} - 1}{0.09}}
\]

\[
\text{Savings Amount} = \frac{7,021,265}{\frac{5.6044 - 1}{0.09}}
\]

\[
\text{Savings Amount} = \frac{7,021,265}{51.1602} \approx 137,244.36
\]

Thus, Vikas needs to save approximately **Rs.137,244** annually to achieve his retirement goal.

---

### Summary of Results:

1. **Vikas needs Rs.7,021,265 in his investment account by the age of 60** to fund his retirement withdrawals.
2. **He should save Rs.137,244 annually for the next 20 years** to reach this target.

---

Would you like further details or have any questions? Here are some related questions to consider:

1. How does the inflation rate impact Vikas' retirement savings plan?
2. What if Vikas expects to live beyond 75 years?
3. How would an earlier retirement age affect his savings requirement?
4. What would be the impact of a higher or lower annual return on his savings?
5. How can Vikas adjust his savings plan if his salary increases at a different rate than expected?

**Tip:** Regularly review and adjust your retirement plan to account for changes in income, expenses, and market conditions.

Explore how to calculate retirement savings and investment needs for Vikas based on his current financial situation. Learn about annuities, compound interest, and financial planning strategies. Includes detailed calculations and solutions.

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