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.

Select what do you want to find:
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Results:

Future Value:
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Total Principal:
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Total Interest:
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Balance by Year

Learn how we calculated this below


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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.

But 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.

Would you rather receive $1,000 today or $1,000 one year from now? The answer is simple. You would want to receive the money today. Even if you invested it at a risk-free rate of 1%, that would give you $1,010 at the end of the year.

However, would you prefer to have $1,000 today or $1,100 one year from now? We can’t answer that unless we know 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, but there is a word of caution when selecting different rates of return. We are assuming that the rate of return is given and will occur exactly as we plan, which is not always the case.

If you set your rate of return at 10% because a particular investment has historically yielded a 10% return, that doesn’t mean it will earn exactly 10% year in and year out. Some years it might be a 0% return or even negative, while some years, it might be 20% or higher.

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 the variable, the other four variables must be known.

The interest rate and number of periods are the exceptions because they don’t always need a payment value to solve for them, and a payment value is not needed in the time value of money calculator.

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 in for 30 years, the investment has grown by over 1,600%. This is exponential growth.

Compound interest, along with investing early and making steady payments into a retirement account, has 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.

Time Value of Money Formula

The time value of money formula can be found below. Specifically, this is how you would 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

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} + PMT \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.