Question

You are planning to save for retirement. You would like to retire 20 years from today and you currently have $190,000 set aside. You anticipate saving $825 per month ($550 out of your pocket and $275 from a company match into your 401(k) plan. You anticipating earning an 8.5% rate of return over the next 10 years. After 10 years, you will up your monthly savings to $X per month (combined contribution from you and your employer into your 401(k) plan) over the last 10 years of your savings period. During this 10 years, you will lower your risk-return strategy so that the expected return will be 7.8%. Once you hit retirement, you want to take out $170,000 on the day you retire. After that you will take out money at the end of each year as follows: Years 1-5 $100,000 per year Years 6-11 $120,000 per year Years 12-25 $110,000 per year Finally, you want to have $270,000 remaining at the end of the 25-year retirement period and you anticipate earning 4.6% per year in retirement (Hint: Note that the $270,000 remaining is at year 25 of the retirement period so that your year 25 CF is actually $380,000 – the last $110,000 plus the $270,000). Figure out how much you need to save per month over the final 10 years leading to retirement in order to meet your plan.

Answer 1

For solving the problem, all cash flow shall be computed at Yr 20 i.e.

1. All future outflows to be discounted at 4.60% to get present value at Yr 20

2. Future value of all monthly contribution of $825 from Yr 1 to Yr 10 to be computed till Yr 20

3. Future value of initial investment of $190,000 to be computed till Yr 20

4. Future value of all monthly contribution of $X from Yr 11 to Yr 20 to be computed till Yr 20