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Question about calculating monthly savings to reach retirement with inflation

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  • Question about calculating monthly savings to reach retirement with inflation

    How do I calculate the amount I need to save for retirement taking inflation into consideration?

    For example, let's assume I need my investments to provide $100,000 per year for 30 years once I retire at the age of 60. Assuming a 4% withdrawal rate, I need $2,500,000 in my retirement nest egg. Let's say I'm 30 years old, so I have 30 years to save and invest in order to reach $2,500,000. Let's assume I achieve a lifetime real return of 6% per year.

    How do I calculate how much I need to save in order to reach my goal of $2,500,000? Do I simply use a compounding interest calculator such as this on bankrate.com and just plug in my variables?

    Another question is how do I factor inflation into all of this? Saving x dollars per month in order to reach a nest egg of $2,500,000 is only applicable in 2017 dollars, but not in 2047 when I will retire in the example I gave.

  • #2
    Getting into some financial modeling here, so keep in mind you need to create some assumptions and then relax them to test for what wiggle room you have.  The first thing is - yes - calculate how much you'll need for retirement.  You are basing that off of 100k of income in 30 years.  To determine what that is in present value terms you need to discount that back by inflation.  All the statements are to be typed into Excel.  If you *assume* that inflation will be 2.5% that means your present value is:

    =pv(0.025,30,0,-100000) = $47,647

    So that means you're assuming that you'll be living off the equivalent of $47,647 in today's dollars in the future.  Keep in mind, that's before any taxes.  Is that what you and your (assumed) partner will be comfortable living off of on a pre-tax basis?  If not, you need to determine in today's dollars (Present Value) what you would need, assuming any additional expenditures for fun, subtracting out expenses you think will be a non-issue (kids, mortgage, etc.).  Then, do the Future Value (FV) calculation in Excel to determine what you'd need to live off in 30 years.  Let's say you think you'll actually want to live it up a little and spend $70,000 in today's dollars.  That would be:

    =fv(0.025,30,0,-70000) = $146,830

    See how much things can change based on a few assumptions?  So now you're at year 60 on your timeline and you think you'll expire 30 years from there.  Next you need to determine your rate of return on that nest egg (assumed of course), the growth of the annuity (since after all, inflation hasn't stopped just because you retired), and how much you want to leave behind (residual value, or future value at age 90).  If you assume a constant annuity stream of payments of $146,830 a year for 30 years you'll underestimate your needs or will undershoot your residual value, or perhaps go broke before retirement.  Assume you'll be conservative and have a 40/60 stock/bond portfolio that gets you 4% annually.  Inflation is still 2.5%.  You want to leave $2,000,000 to your heirs.  To determine the PV at age 60 that you'll need to accomplish this it's a 2 step process.  The first is to determine your PV of a growing annuity.  I don't think Excel has this calculation but you can find it here:

    http://www.financeformulas.net/Present_Value_of_Growing_Annuity.html

    This just calculates the PV of the growing annuity streams (your draw-down of $146,830 growing by inflation every year, with the corpus growing at a given rate as well).  I get $3,458,148 for this annuity stream w/ growth.  The second step is calculating the PV of the $2,000,000 you want to leave behind in 30 years.  For that you do:

    =pv(0.04,30,0,-2000000) = $616,637

    So, the total you'd need with these assumptions at age 60 is:

    $3,458,148 + $616,637 = $4,074,785

    Ok, so you need to have a little over $4M by age 60 to get you to your goals.  Your question was about inflation and regular savings.  That $4M (we'll just call it this to make things simple) is your future value (FV).  Your present value is how much you have invested now (let's assume you have nothing invested now for simplicity).  Here is the key to answering your question.  You have to assume a nominal rate of return - what you think your asset allocation will get you on a compounded basis over the next 30 years.  This will vary depending on your risk profile and (obviously) how the market ends up actually performing.  Let's just say 6%.  The inflation rate will destroy your savings' value just as that nominal rate of return will help it, so for simplicity just subtract out the inflation rate from your growth rate = 6% - 2.5% = 3.5%.  This is what is known as the real rate of return.  So you have all the elements of your equation.  You have your FV, PV, rate, periods (30) to get your payment (what you need to save annually).  The calculation is:

    =pmt(0.035,30,0,-4074785,0) = $78,934

    This is a gross estimation of a yearly amount with compounding occurring at the end of the year.  If you want the monthly rate of savings and compounding you need to convert that yearly rate of 3.5% into an APR then divide by 12 to get your monthly rate, then you'll change your periods to 30x12 to get the number of months (rate needs to match the period).  Before committing to $79k of saving a year I'd adjust some of your assumptions to see what wiggle room you have.  You might not be comfortable with the effects of 3% inflation.  I'd be conservative.  The art of pessimism - you're either right or pleasantly surprised.  Good luck.  Hope this helps.

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