The Time Value Of Money With Exercises

Last Updated on July 8, 2021

In this post, you will learn more about the time value of money or simply put how time can work in your favor by increasing the value of our money. The minimum goal of each individual should be to achieve a return that covers inflation and the cost of investing that money to preserve the value of the money earned.

To accomplish this, you must first understand the impact that time has on money through inflation which you could learn about in a previous post. If you didn’t read it, I strongly recommend doing it here before reading on.

We will start with the simplest formulas and gradually move towards more complex ones. In short, the more complex the formulas, the higher the yields, so it becomes more and more exciting.

Time Value of Money With Simple Interest

Let’s start with a simple interest rate. Imagine that you have a term deposit of 10,000 euros in a bank for one year at an interest rate of 3%.

To calculate simple interest we use the following formula:
A = P (1+r)

A = the future value of the investment
P = the principal investment amount
r = the interest rate (decimal)

If you include the amount in the mentioned formula, you will get that the total return on investment is 10,300 euros. After a year, you earned 300 euros in interest. Suppose that inflation was 2%. The real yield you achieved that year was 100 euros. In addition to protecting your money from inflation, you also achieved a return of 1%.

Not bad, considering that this is a simple and safe form of investment. But interest rates on deposits largely depend on trends in the economy. Today, it is difficult for banks to offer such a generous interest rate on term deposits. At the time of writing, all commercial banks can borrow from the central bank (eg FED, ECB) at rates less than 1%, so they have no reason to give individuals higher interest rates. But that’s a topic for another time.

Time Value of Money With Compounding Interest

Now that you know what a simple interest is, let’s see what your yield in a complex interest account would look like. We will use the same attributes from the previous example. This time we want to deposit that amount for 3 years by reinvesting the interest each year. How much money will you have after 3 years?

Since we have reinvested all interest earned, we must use the following formula for compounding interest:

A = P (1+r)^n

We’ve added an “n” attribute that means:

n = the number of times that interest is compounded per period

In case you raise the interest you earned every year, you would not profit from the reinvested interest. In that case, you would stay shorter by the amount of 27 euros after three years.

Therefore, it is actually interest on interest which is a very powerful tool for earning. Einstein called it the eighth wonder of the world, hence his famous sentence.

Albert Einstein once noted that the most powerful force in the universe is not the gravitational force but the power… | Einstein, Compound interest, Albert einstein

Although you are now thinking that this is not a drastic difference, 27 euros after three years for such amount, nothing special. I agree, but rarely has anyone gotten rich in such a short term and with such a low interest rate.

In this example, we were talking about preserving the value of money from inflation. The money we keep in the bank has very little risk (it is almost non-risk). Therefore, we cannot expect to have phenomenal returns on investments.

What we need to do for a higher return is to increase the investment horizon and choose alternative financial instruments to increase our return.

Compounding Interest – Real Example

Let’s say you decide to invest in the S&P 500 index which we’ll talk more about in another article. In short, It’s a stock index that tracks the 500 largest companies in the United States. In the investment world, numerous studies have shown that it is wiser for the average investor to invest in the S&P 500 index than to choose stocks on their own. The reason is that professional investors fail to beat the S&P 500, which averages about 7% after inflation.

Back to the example, here we are talking about a more complex formula with periodic payments. Therefore, I made the following calculator:

[CP_CALCULATED_FIELDS id=”7″]

Let’s look at what your return on the S&P 500 index would look like if you initially invested € 10,000 with periodic payments of € 1,000 per month over a 20-year period. The final amount you would get is 561,314 euros.

In the chart below, you can see how much of that amount you invested during the year. Also, you can see the proportion in the total amount related to interest.

So, over 20 years, a total of 250,000 euros has been invested, and the total interest obtained is 311,314 euros. You earned more than double the amount. If you divide 311,314 euros by 20 years, you get the amount of 15,565 euros per year.

This is a real example of how money makes money and it’s like you’ve hired another self to work for you. Of course, for some, this may be an over-optimistic scenario and they are not able to invest 1,000 euros a month, but even if you invest less you will be very grateful after a certain period of time, and you will know that you are getting richer every day. Imagine going to bed knowing every day you are richer, not bad right?

Conclusion

I strongly recommend that you go through this lesson multiple times and don’t go any further until the compounding effect is completely clear to you. You have learned that simple interest is good, but God, you really need that compounding interest rolling in life and you need it now.

Although here we are talking about the compounding effect in finance, use this formula for all other segments of your life. A little progress each day adds up to big results.

There is never enough learning and repetition, so I suggest you read an article from Investopedia on the same topic that you can find at this link.

In the next post, you will learn to set financial goals based on the time and risk you can take. After that, you will see what kind of investments would be most appropriate for you.

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