Do the Math: Annual Savings Needed to Reach Nest Egg Goal

Question: Tom is 50 and has $100,000 saved for retirement. He'd like to retire at 60 and wants to have $1,500,000 in the bank by then. Assuming his savings earns an average annual after-tax rate of return of 7%, how much does Tom have to put away each year to have $1.5 million in 10 years?

Answer: The first question to answer is what the $100,000 already saved will be worth in 10 years. To determine this, we use the following equation:

F10=F0 (1+i)10
Where    F0    =    $100,000
i    =    7%
F10    =    Value of $100,000 in 10 years
So    F10    =    F0 (1+i)10
=    $100,000 (1.07)10
=    $100,000 x 1.967
=    $196,700

Note: 1.967 can be obtained by doing the math, or by simply using a present-value table. See present-value factor table provided adjacent to this article. Locate the intersection of 10 years (periods) and 0.07 rate of interest, and you will find 1.967. Multiply this by F0 and the result is $196,700.
So we can expect the currently saved $100,000 to be $196,700 when Tom reaches 60. His bogey is $1,500,000, so he needs to know how much money he has to stash away in each of the next 10 years to make up the $1,203,300 shortfall ($1,500,000 minus $196,700).

Let's label the $1,203,300 bogey R.

R = $1,203,300
Let's label the interest rate i.

i=7%
Let's label the required annual contribution P.

P=?
The number of years available we'll label n.

n=10
So here's the formula:

P=(R * i)/[(1+i)n - 1]
Solving for P:

P    =    ($1,203,300 * .07)
(1 + .07)10 - 1
=    $84,231/(1.0710 - 1)
=    $84,231/(1.967 - 1)
=    $84,231/0.967
=    $87,105
So for Tom to reach his goal of $1,500,000 in savings in 10 years, he has to invest $87,105 per year and earn an annual rate of return of at least 7%. The problem is that 7% after-tax rate of return is rarely achievable without taking a lot of risk - not recommended with retirement funds. But if the funds are in retirement accounts, then they are tax sheltered, and pretax return is the same as after-tax return. Pretax return of 7% is much more easily achieved. So he needs to get all this money into tax-sheltered retirement accounts. Assuming the $100,000 is already in such an account, all he has to do is place his annual savings into the same.

Is this possible? Take a look at the chart on page 13. Do you see the annual contribution limits for various retirement plan types? The only plan that will allow an annual contribution as high as $87,000 is the defined contribution plan. Talk to your financial advisor about putting one in place.

Future value interest factor of $1 per period at i% for n periods, FVIF(i,n).
Period    4%    5%    6%    7%    8%    9%    10%
1     1.040     1.050     1.060     1.070     1.080     1.090     1.100
2    1.082     1.103     1.124     1.145     1.166     1.188     1.210
3    1.125     1.158     1.191     1.225     1.260     1.295     1.331
4    1.170     1.216     1.262     1.311     1.360     1.412     1.464
5    1.217     1.276     1.338     1.403     1.469     1.539     1.611
6    1.265     1.340     1.419     1.501     1.587     1.677     1.772
7    1.316     1.407     1.504     1.606     1.714     1.828     1.949
8    1.369     1.477     1.594     1.718     1.851     1.993     2.144
9    1.423     1.551     1.689     1.838     1.999     2.172     2.358
10    1.480     1.629     1.791     1.967     2.159     2.367     2.594
11    1.539     1.710     1.898     2.105     2.332     2.580     2.853
12    1.601     1.796     2.012     2.252     2.518     2.813     3.138
13    1.665     1.886     2.133     2.410     2.720     3.066     3.452
14    1.732     1.980     2.261     2.579     2.937     3.342     3.798
15    1.801     2.079     2.397     2.759     3.172     3.642     4.177
16    1.873     2.183     2.540     2.952     3.426     3.970     4.595
17    1.948     2.292     2.693     3.159     3.700     4.328     5.054
18    2.026     2.407     2.854     3.380     3.996     4.717     5.560
19    2.107     2.527     3.026     3.617     4.316     5.142     6.116
20    2.191     2.653     3.207     3.870     4.661     5.604     6.728
25    2.666     3.386     4.292     5.427     6.848     8.623     10.835
30    3.243     4.322     5.744     7.612     10.063     13.268     17.449
35    3.946     5.516     7.686     10.677     14.785     20.414     28.102
40    4.801     7.040     10.286     14.974     21.725     31.409     45.259
50    7.107     11.467     18.420     29.457     46.902     74.358     117.391