Question

Imagine you are 25yrs old and earning $50,000 per year. You think smartly that you would like to do some long-term retirement planning and begin to brainstorm with yourself as to what you should do. You decide that having $50,000 per year in retirement would be a good and that you expect to work until 65 and plan on being retired for 30 years.

How much do you expect to reasonably save as a percentage of your salary?

And what interest rate do you need to achieve during your working years and retirement years such that your plan will work. (it should be the same)

(complicate the scenario by things you cannot control (inflation, future earnings increases, wars, economic recessions, and the death of you favorite rock star) and you are sure to give up in exasperation. So don’t. keep everything static.

Answer 1

The time line for the given question can be seen below:

• Generally, according to long term buy and hold investors, the US stock market earns about 10% p.a.
• Also, the general inflation rate in US in the year 2018 was about 2%.

For this reason, our return on investment (ROI) shall be 10% p.a. and inflation at 2% p.a.

For our retirement, we will be requiring $50,000 per year. Using the ROI as 10% and inflation rate at 2%, we can calculate the present value of the corpus required to fund $50,000 per year (for 30 years post retirement).

PVA = A* ((1/r)-(1/(r*(1+r)^n))

PVA = 50,000* ((1/0.10)-(1/(0.10*(1.10)^30))

The present value comes up to $471,345.72.

Thus, at 65 years of age, we shall have $471,345.72 to fund $50,000 per year for the retirement period of 30 years. This is our retirement corpus.

To find how much we need to save each year from age 25, we shall use the FVA formula:

FVA = A*{[(1+r)^n]-1}/r

Here we need to find the Annuity (A) amount.

$471,345.72 = A*{[(1.10)^40]-1}/0.10

A = $ 1,064.97

We will thus need to invest $ 1,064.97 each for forty years from age 25-65 at a ROI of 10%, to withdraw $50,000 each year for thirty years from age 65-95.