You are doing some long-range retirement planning. On the day you retire (23 yea

Question

You are doing some long-range retirement planning. On the day you retire (23 years from now) you want to be able to withdraw $200,000. Then, you want to withdraw the following amounts at the end of each year after that (during your retirement period).

                                Years 1-4              $160,000

                                Years 5-9              $175,000

                                Years 10-15         $165,000

                                Years 16-26         $145,000

At the end of the 26th year in retirement, you’d like to have $500,000 remaining in your retirement account available for withdraw. During your retirement years, you anticipate earning a 4.5% rate of return.

You currently have $275,000 that you are going to use to start your retirement savings today. In addition, you plan to save $700 at the end of each month for the next 8 years. At that point (8 years from today) you will add another $150,000 to your retirement fund. Then, over the remaining 15 years, how much must you save at the end of each month to reach your goal if you earn 8.9% as a rate of return during the first 8 years and 7.6% over the final 15 years in which you are saving for retirement?

Explanation / Answer

The solution can be derived in 3 broad steps:

Step 1: Estimating value of post-retirement cash flows at the end of 23rd year

Block 1: Years 1-4:   Finding the present value of $160,000 per year for 5 (cash inflow at year end) years @ 4.5%. Using a financial calculator or using this in Excel =PV(0.045,5,160000), we get $ 702,396

Block 2: Years 5-9: Here the PV obtained will be at Year 5. So PV of $175,000 per year for 5 years @ 4.5% =PV(0.045,5,175000), we get $ 768,245. Converting this to PV at beginning of retirement = 768,245/(1.045)^5 = $616,479

Block 3: Years 10-15: =PV(0.045,5,165000) =$724,346. At beginning of retirement = 724,346/(1.045^10) = $466,426

Block 4: Years 16-26: =PV(0.045,10,145000) =$1,147,344. At beginning of retirement = 1,147,344/1.045^16 = $567,326

Hence total amount required at beginning of retirement = $702,396 + $616,479 + $466,426 + $567,326 = $2,352,627

Step 2: Estimating future value of savings till retirement

a) Now $275,000 @ 8.9% per year for 8 years and 7.6% thereof will be worth 275,000 * 1.089^8*1.076^15 = $ 1,632,073

b) $700 per month = $5600 per year for 8 years. This will yield 5600 * (1.089^8) = $11,076 at the end of 8 years which will amount to 11,076 * 1.076^15 = $ 33,232 at the beginning of retirement.

c) Lumpsum of $150,000 at the end of 8th year will be worth 150,000 * 1.076^15 = $ 450,065

Hence total available at the beginning of retirement = $ 1,632,073 + $ 33,232 + $ 450,065 = $ 2,115,370

Remaining needed = Total needed - Total available = $ 2,352,627 - $ 2,115,370 = $ 237,257

Now this has to be saved every month for 15 years at 7.6% per annum. Converting this into annual amount, Let this annual amount be k.

k * 1.076^15 = 237,257. Solving for k we get k = $79,074 per annum which means you will have to save 79,074/12 = $ 6,589 per month

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