Why Save? The Time Value of Money

Steven Xu
40 Years in 40 Pages
3 min readOct 17, 2014

When thinking about retirement savings you must understand the time value of money. This is the concept that money today is worth more than the same amount of money in the future. The reason lies in current earning potential. A core principle of finance, this asserts that given an investment opportunity, money is worth more sooner rather than later. An example makes this much clearer:

Let’s assume that over the course of one year (n=1) you can earn a growth rate r, say 5%, through investments be they stocks, bonds, or other investments you find. This means that $100 today (in terms of present value or PV) will be $105 one year from now (the future value, or FV). All right, but how do you value how much $100 a year from today is worth to you right now? Using the same 5% rate you could earn over one year, $100 in the future is worth only $95.24 today (Future value of $100 divided by the growth rate of 5%). This is called discounting, or the process of determining the present value of a payment (or payments) received in the future.

This same process can be used in the opposite way and is the main focus of this chapter. Instead of evaluating how much a future payment is worth to you today, you want to know how much your nest egg will be when you decide to retire. In the same idea that $100 a year from now is worth less today, $100 two years from now is worth even less than $100 one year from now. But remember, we’re focused on turning present value into future value. Using the above example, this means that $100 today could be $105 one year from now ($100 x 1.05), but two years from now it will be worth $110.25 ($105 x 1.05).

Compound Interest

Compounding is the act of generating growth from previous earnings. If you save $3,000 a year between the ages of 20 and 65 you have $135,000. But what if you earned 7% every year by investing that $3,000 instead of saving it?

That’s a total savings of $3,210 ($3,000 * 1.07) the first year,

$6,644.7 (year 1 contribution of 3,434.7[$3,210 * 1.07] + $3,210 [year 2 contribution]) the next year, and so on.

The money you earn through your investments begin to earn returns as well. Compared to savings of $3,000 and $6,000 if you just stowed the money in a bank account vs. investing with retirement in mind.

If the trend continues, you would earn

$722,247.93

from investments for a total value of $857,247.93 when you retire. Imagine if you contributed more than $3,000 a year (this is extremely doable in most cases). If you wait just 4 years and begin at age 24, you will have saved $123,000 and earned $520,828.71 for a total nest egg of $643,828.71. Still quite hefty, but just because you didn’t contribute $12,000 over the course of 4 years you have over $200,000 less than if you had started earlier. There are two actions you can take to reach a satisfactory value for your savings.

  1. Start early. From the data displayed it becomes overwhelmingly clear that the earlier you start the more time your investments have to grow.
  2. Invest regularly. Keep in mind what you’re saving for. Make sure to stay disciplined in your annual budget and remember to allow for retirement investments. Make it a priority to maximize your contributions as your income allows, you will thank yourself in the future.

We've established that saving for retirement is only beneficial due to the growth potential of our savings. This is to answer the question when to start, and next we will answer how to start.

The next best thing to starting early is starting now.

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Steven Xu
40 Years in 40 Pages

Alum @UW, Finance @Microsoft, writes about personal finance, the future, and trying to be a better person.