Receiving a payment today is better than receiving one a year from now, in part because the general rate of inflation (e.g., two percent) makes the money worth less next year due to decreased purchasing power (that is, two percent less). It is also better if you are going to save or invest that money, putting it into a savings account at 3% interest (for example) means that in a year you will have an additional earning of 3% on top of the original amount. We can illustrate it in this equation:
Pyear1 is the principal amount you received at the beginning of year one, and Pyear2 is the principal amount you will have at the beginning of year two, including the interest you earned. However, interest or dividends money in savings or an investment is compounded. That is, if you leave the interest or dividends you earned over year one in savings for year two, you will again receive 3% interest on the principal plus 3% interest on the interest you already earned in year one. We can represent this mathematically as follows:
Let’s say that you put $1,000 in a savings account at 3% interest and leave it to compound. Below, you can see the amounts you will have at the beginning of each year:
The compounding of the interest may not seem like a lot here, but it makes a huge difference when you are saving for retirement. For another example, let’s say you start working at 21 and retire at 68, spending 47 years in the labor force. As we will discuss in more detail later, one investment in a mutual fund with a widely diversified portfolio saw a return of an average of 10.1% per year for ninety-four years. If you were to invest $1,000 in this diversified portfolio and did not touch it for 47 years, you would have a retirement nest egg that looked like this:
- Original Amount: $1,000.00 at beginning of year 1
- Interest Rate: 10.1% compounded
- Time Period: 47 years
- Amount at end of 47 years: $92,045.80
Furthermore, you will most likely deposit more into your retirement account each year, rather than just $1,000 once at the beginning of your career. If you invested $1,000 per year each year in this diversified stock portfolio, at the end of your career your nest egg would look like this:
- Principal Amount: $1,000.00 each year invested at the beginning of each year
- Interest Rate: 10.1% compounded
- Time Period: 47 years
- Amount at end of 47 years: $1,084,535.20
Most of the time, if you work for a good employer, they will sponsor a 401(k) retirement plan and match your contributions. The most common plan is that you contribute 3% of your salary and your employer matches. Let’s say that together you contribute $4,000 per year for 47 years and put it all in a diversified stock portfolio. In that case, here is your retirement nest egg:
- Principal Amount: $4,000.00 each year invested at the beginning of each year
- Interest Rate: 10.1% compounded
- Time Period: 47 years
- Amount at end of 47 years: $4,338,140.81
This is also tax free until you retire and withdraw money to live on.