Investing Fundamentals

Understanding The Time Value of Money Formula


A dollar today isn’t the same as a dollar tomorrow, that’s the time value of money. Risk and return are expecting a dollar risked to earn more than a dollar.

The time value of money and risk and return are two core concepts in personal finance. Luckily, each boils down to a pretty simple statement.

The time value of money means your dollar today is worth more than your dollar tomorrow.

Risk and return say that if you are to risk a dollar, you expect gains of more than just your dollar back. For each unit of risk you take on, you expect a slightly more significant unit of return.

Even though these concepts are easy to simplify, I want to dig a bit deeper into each of them.

Time Value of Money

Today’s dollar is worth more than tomorrow’s because of inflation (on the side that’s unfortunate for you) and compound interest (the side you can make work for you).

Inflation pushes prices up over time which means that each dollar you own today will buy more now than it will in the future. This is why investing is so important.

Inflation is reported on an annualized basis. That means that to invest a dollar today, you’d have not only to expect to exceed inflation but also have some wiggle room to account for the uncertainty of the future.

Over time the stock market beats out inflation. So if you put the same amount of money in a savings account and investment account, the money invested would be worth far more than the money sitting in the savings account.

Opportunity Cost

For every choice made, there are choices sacrificed. The choice to go to college is an excellent example of opportunity cost.

Choosing to attend means you are giving up four years worth of salary you would have earned at a job and four years of work experience.

Of course, you hope that by choosing to go to school, you will make more money over your lifetime than if you don’t attend. So it’s a gamble, but a calculated one that hopefully has a more significant pay off eventually than if you had chosen not to go to college.

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Compound Interest

What’s the point of investing money if it won’t grow faster than inflation? You’d be better off spending it now when it has a higher value. That’s where compound interest comes to the rescue.

A standard bond returns a flat percent of the face value each year, which is simple interest. In that case, if you got 5% on a $1000 face value bond, you’d get $50. That’s not bad, but it’s not where the magic lies.


When you’re looking at investments like stocks, you expect them to grow approximately 5% a year, or 7% if you count dividends. If you have a $100 stock that increases 5% by the end of the year, you have $105.

By the end of year two, it’s grown another 5% and is worth $110.25 ($105*1.05). While that’s only an extra 25 cents, in this case over long periods of time and with larger dollar amounts, that can end up being a lot of money.


Time Value of Money Calculator

Assuming you have a financial calculator or access to the internet, it’s pretty easy to see how much your current dollar would be worth tomorrow, though you do have to make some assumptions.

If you’re not a money nerd like me and don’t have a financial calculator sitting next to you, I recommend using this calculator from Zenwealth. If you’ve never used one before, the interface can be somewhat confusing so here’s what the abbreviations and terms mean:

PV: This means present value. Enter how much money you have today. If you have a $20 in your wallet, enter 20.

Rate: this is the rate of growth. If you’re calculating how much inflation will be, you can use a number like 3%. If you’re trying to see what your money will grow if you’re getting a 7% real (after inflation) rate of return use 7%. You put in the whole number (7) instead of the actual decimal-y number (0.07).

PMT: This means payment. It’s the amount that you’re adding to the PV per period. Think of it as a monthly contribution to an IRA (assuming you’re doing monthly compounding).

Periods: The number of times you’re compounding your money. It’s important to keep in mind how extended a period is- are you compounding weekly, monthly, annually, weekly?

FV: This is your future value. If you’re trying to calculate what your money will be worth in the future once you’ve made payments and had to compound, you’ll see your answer here. If you’re trying to reverse engineer what a future amount of money is worth today with deflation, you start with this number.

time value of money formula

Using the Time Value of Money Formula

Are you bored yet? I promise you it’s essential. With those variables you can answer questions like these:

How much money would I need to save starting today if I wanted to have $1,000,000 in 20 years assuming 6% growth after inflation?

Enter 6% for rate, nothing in payment, future value $1,000,000, present value $0, and 20 periods. Please, try it yourself! You could do this for anticipated future costs like weddings, school costs, buying a house or car, or anything else you want to save for over time.

If I start with nothing today and put away $100 a month, what will I have in 10 years if I get 4% growth after inflation?

Here we use present value 0, payment 1200, rate 4, ten periods, and solve for future value. Again, I recommend you try it yourself, but I get $14,407. This kind of question is great for seeing where you’ll be if you start today.

I go through these kinds of hypotheticals occasionally because it’s always fun to watch how my money would work for me.

One important note when working with the calculator is that either present value, future value, or payments are a negative number or 0.

A negative denotes a cost, so a negative payment is a payment into the account and a present negative value means you paid into it with your own money. It’s what you need to do to buy the future value.

Risk And Return

Now that you can calculate the time value of money, it’s time to look at risk and return. From example 1 we know that you would need to save a whopping $2,308 per month to get from $0 to $1,000,000 in 20 years with 6% growth.

If you’re like me, that number seems pretty high. We need to look at securing a higher rate of return to drop that amount. A 2% higher return would drop the monthly savings by $500 but what does that mean for your investing strategy?

But, you’re unlikely to get extra return without taking on extra risk. Investing in a small startup is a bigger risk than investing in a well-established company, but the investment in the startup has the potential for a bigger payoff.

It’s essential that you are comfortable with and aware of the amount of risk in your investing strategy. If you can stomach the lows and highs that come with extra risk, it could make sense to strive for the extra return and in turn, lower your monthly payment value.

time value of money start early

Why This The Time Value of Money  Important

These concepts are the basis of every recommendation you see, even if the person making the recommendation isn’t explicitly aware of it.

It’s better to invest early because of the time value of money concept. Each dollar that you invest now has time to grow, but the reason that it’s important to invest that dollar instead of sitting on it is that if it doesn’t grow and outpace inflation, you will lose purchasing power over time.

Gas, movie tickets, and food used to cost less and a $50,000 salary used to mean a lot more. That fantastic investment that promises a huge return? It comes with increased risk as well, or it would have been snapped up already.

Again, that doesn’t necessarily mean it’s a bad decision; you just need to understand what you’re getting in to. You need to take some risk for your money to outpace inflation so just make sure you’re comfortable with the amount you’re taking.

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