I hope that after I die, people will say of me: "That guy sure owed me a lot of money."

## Introduction

I have had a number of posts recently on saving for retirement. These posts ALWAYS follow discussions I have had with my family on the importance of starting to invest early – both for retirement and general financial health. I do not want my family members to get to retirement without an investment portfolio (Figure 1), a situation that I have seen and is not pretty.

Yesterday, my wife was told at an investment seminar that we should have 11 times our annual income in retirement savings. The same day, I saw an article on the Fidelity web site that recommended 8 times our annual income in retirement savings. As for me, I routinely tell my sons that they will need at least 20 times their annual incomes. Each of these rules is correct in the proper circumstances.

There is no mystery here – as I always say, the answer to all life's interesting questions is "It depends ...".

## Background

### Objective

I will demonstrate how to derive these retirement multiples for yourself using some basic financial mathematics. This knowledge will allow you to change the assumptions as you require for your situation and you can make your own retirement multiple rule of thumb.

### Analysis Caveats

My focus here will be on 401K retirement plans because I want to make sure that my sons take advantage of their employers matching plans. Since 401K plans use deferred income, this income is subject to taxes. My analysis assumes that your retirement tax rate is the same as your working tax rate. That may or may not be true. For example, many retirees have paid off their home mortgage and do not have mortgage deductions anymore.

I do not model the effect of inflation once you have retired. We now see people retired for twenty to thirty years and inflation will have an impact.

Young people need to decide if they think Social Security will be there for them. I sometimes wonder if it will be there for me. My sons should plan as if it will not be there.

### Definitions

There are a some terms that will be important in the analysis to follow.

- Retirement Multiple (Symbol:
*M*) - The amount of retirement savings needed at the time of your retirement expressed as a multiple of your working income at the time you retire. So if you make $100K annually at the time you retire and you have saved $800K, your retirement multiple is 8.
- Replacement Income Percentage (Symbol:
*K*)_{R} - The percentage of your working income that you will require during retirement. For the discussion here, I will assume that you need 85% of your working income while in retirement. I base this number on my assumption that at the time your retire you will be putting 15% of your working income into retirement investments and these investments will cease when you retire.
- Number of Annual Payments (Symbol:
*N*) - The number of investment payments made per year. I will assume one payment month or 12 per year.
- Number of Years in Retirement (Symbol:
*Y*) - For this calculation, I will assume my pension investment must provide a fixed income for 25 years, say from age 67 to age 92 − no one lives forever.
- Annual Rate of Return (Symbol:
*R*)_{A} - This is the rate of return I expect on my retirement investments annually. For my analysis here, I will assume
*R*=6.0%, which is a commonly used value._{A} - Rate of Return Per Payment (Symbol:
*R*) - This is the rate of return per payment period, which is given by the formula .
- Inflation Factor (Symbol:
*K*_{I}) - This represents the loss of purchasing power per dollar from the time of retirement planning to retirement. I will assume that you will plan your retirement at age 30 and retire at age 67 − the case for one of my sons. I will also assume that you will average 2.3% annual inflation over your work life. Some
*R*values assume inflation while others do not._{M} - Non-Investment Income Percentage (Symbol:
*NI*) - Many retirees will have Social Security income or pensions. This income will reduce the amount of money you need to get from your investments. Note that Social Security payments are adjusted for inflation and pension payments are usually not. Some
*R*values assume non-investment income and others do not._{M}

## Analysis

I will be using Mathcad's Present Value (PV) function for the following work, however, Excel has the same function and you can easily perform the following analysis using Excel's PV and goal seek functions.

### Formula Derivation

Figure 2 shows how to derive the key relationship for determining your retirement multiple, which really is just the standard present value formula for an annuity due. The formula I will be using is highlighted in yellow.

### Derive 8x Rule

We can compute *R _{M}* = ~8 by assuming a nominal non-investment income (

*NI*=25%) and no inflation (

*K*=1). We can substitute these values into the formula of Figure 2 as follows, which gives us a retirement multiple of ~8.

_{I}An *M*=8 is appropriate for people near retirement who expect Social Security and pensions. Since these folks are near retirement, inflation will not have time to significantly impact your planning.

Since few people receive more than $2K per month in Social Security, this calculation means that your retirement income is capped around $96K per year, which is a lot for a retiree.

### Derive 11x Rule

We can compute *R _{M}* = 11 by ignoring non-investment income (

*NI*=0) and inflation (

*K*=1). We can substitute these values into the formula of Figure 2 as follows, which gives us a retirement multiple of ~11.

_{I}*M*=11 is appropriate for people who are near retirement and do not want to count on any Social Security income. It is a conservative approach to retirement planning, but can be justified.

### Derive 20x Rule

We can compute *R _{M}* = 20 by assuming a nominal non-investment income (

*NI*=25%) and inflation (). We can substitute these values into the formula of Figure 2 as follows, which gives us a retirement multiple of ~20.

*M*=20 is appropriate for young people that will be investing for many years and will experience significant inflation. This number also assumes Social Security will be there for them, which may not be the case.

## Conclusion

This quick post summarizes discussions that I had with my wife and sons on retirement planning. I hope it prods some of you into looking at your retirement plans.