# TVM Calculator – Time Value of Money Formula

Use our TVM calculator to calculate future value, present value, payment, rate, or number of periods using the time value of money formula.

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 Future Value: $Total Principal:$ Total Interest: $### Balance by Year Learn how we calculated this below ## On this page: ## What is the Time Value of Money? The time value of money essentially states that the value of money today is worth more than the value of money in the future because you can invest money today and earn a return on that money. However, if the money was received in the future, you wouldn’t be able to invest the money between today and the time it was received, so you would earn less. ### Key Points • The concept of the time value of money is that money today is worth more than money in the future because you can invest money today and earn a return on that money. However, if the money was received in the future, you wouldn’t be able to invest the money between today and the time it was received, so you would earn less. • The factors that contribute to the time value of money are the future value of that money, the present value, the payments made, the interest rate earned on the investment, and the number of periods or years that it’s invested. • The number of compounding periods can change the time value of money drastically. The more frequent the compounding, the higher the interest earned will be and the higher the future value. • The time value of money has a negative relationship with inflation, which means that as inflation increases or prices increase, the purchasing power or value of money decreases. To help understand the time value of money, think about whether you would you rather receive$1,000 today or $1,000 one year from now? You would want to receive the money today because you could invest that money and earn a return, even if it was only 1%. However, would you prefer to have$1,000 today or $1,100 one year from now? This depends on the rate of return. If you could invest the$1,000 at 5%, you would have $1,050 after a year, so you should take the$1,100 in a year.

But let’s say you could invest at 15%. Then you should take the $1,000 today, invest it at 15% and end up with$1,150 at the end of the year.

The time value of money is a very useful tool for planning purposes, however, we are assuming that the rate of return is known, but this isn’t always the case.

If you assume a rate of return due to historical performance, that doesn’t necessarily mean that will be the rate of return in the future.

It may be more useful to use it for long-term planning because over the long run the actual rate of return will be much closer to the expected rate of return.

## How to Calculate the Time Value of Money

The time value of money can be calculated using either the time value of money calculator above or by using the time value of money formula in the next section.

The five variables that comprise the time value of money are the future value, present value, payment, interest rate, and number of periods. These variables can be solved using the tabs at the top of the calculator above. In order to solve for one variable, the other four variables must be known.

### Time Value of Money Formula

Using these variables, the following formula defines how to calculate the time value of money to solve for the future value when you know the present value, interest rate, payment, and number of periods.

FV = PV \times \left (1 + \frac{r}{n} \right )^{nt} + PMT \times \frac{\left (1 + \frac{r}{n} \right )^{nt} − 1}{\frac{r}{n}}
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where:
FV = future value
PV = present value
PMT = annual contribution
r = interest rate
n = number of times interest is compounded per period
t = number of periods

In the time value of money calculator, there is an option for how often interest is compounded per year. The available options are daily, monthly, quarterly, semiannually, and annually. The more times interest is compounded, the higher the interest will be when solving for the future value or present value.

Our future value calculator and present value calculator will provide the same results that can be found in the TVM calculator above. As you can see below, calculating the time value of money is complicated, so the easiest method is using the calculator.

The main benefit of the time value of money is compound interest. For example, if you invest at 10% for 3 years, your investment would have grown by about 33%. But if you leave that investment for 30 years, the investment has grown by over 1,600%. This is due to exponential growth.

Compound interest, along with investing early and making steady payments into a retirement account, have allowed many individuals to retire comfortably. Our compound interest calculator shows how much compound interest can be earned with different sets of assumptions.

To find the present value or future value of an annuity, try using an annuity calculator, which shows the value of an annuity today or at a future date in time based on a given set of assumptions.

For example, let’s calculate the future value of money with a present value of $1,000, an annual contribution of$100, an interest rate of 7%, and a time period of 10 years. We will use annual compounding.

FV = \$1,000 \times \left (1 + \frac{0.07}{1} \right )^{1 \times 10} + \$100 \times \frac{\left (1 + \frac{0.07}{1} \right )^{1 \times 10} − 1}{\frac{0.07}{1}}
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FV = \$1,000 \times 1.07^{10} + \$100 \times \frac{1.07^{10} − 1}{0.07}
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FV = \$1,000 \times 1.9671514 + \$100 \times \frac{0.9671514}{0.07}
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FV = \$1,967.15 + \$100 \times 13.816448
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FV = \$1,967.15 + \$1,381.6448
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FV = \\$3,348.80
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You might also find our interest calculator useful.

### Why is time value of money important?

The time value of money is important for a few reasons. It helps people investing or saving for retirement understand how to get the most out of their money and plan for the future, it helps businesses understand what potential investments are best for their business, and it helps people understand how inflation factors the value of money.

### What are the five elements of the time value of money?

The five elements of the time value of money are future value, present value, payment, interest rate, and number of periods. Future value is the value of an investment at some point in the future whereas the present value is the value of an investment today.

The payment is the annual contribution to an investment, the interest rate is the rate of return that you earn on your investment, and the number of periods is the total number of years that you hold the investment.

All of these factors and the frequency of compound interest can significantly change the future value of an investment.

### Is time value of money inflation?

The time value of money is not the same as inflation, in fact, the time value of money has a negative relationship with inflation. As inflation increases, the future value of money goes down because inflation reduces the purchasing power of a dollar.

Inflation and opportunity cost both factor into the time value of money. The basis of the time value of money is that a dollar today is worth more than a dollar in the future. This is due to inflation and the opportunity cost of not being able to invest and earn interest on a dollar in the future between now and the future date.

### How is the time value of money used?

The time value of money is used to help people understand how to get the most out of their money and determine what investment is the best option for an individual or a business.

The time value of money impacts savings accounts, retirement accounts, investments, or CDs, and helps people understand the purchasing power of their money now and in the future.