Present value to future value calculator

Created by Tomasz Jedynak, PhD, Piotr Małek and Mateusz Mucha

Reviewed by Bogna Szyk and Jack Bowater

Based on research by

“Financial Management: Theory and Practice“ (2016)

Last updated: Mar 10, 2022

Future value calculator is a smart tool that allows you to quickly compute the value of any investment at a specific moment in the future. You need to know how to calculate the future value of money when making any kind of investment, to make the right financial decision. Usually, you'll use the future value formula when you want to know how much an investment will be worth.

Read on this article to find answers for the following questions:

• What is time value of money?

• What is the future value?

• What is the future value formula?

• How to calculate future value?

• What is the difference between future value and present value?

• How can you use future value when making wise financial decisions?

And last but not least, in the text below, you will find out how to use our incredible future value calculator to make your financial decisions faster and smarter.

The time value of money

When explaining the idea of future value it is worth to start at the very beginning. First of all, you need to know that the underlying assumption of future value is the concept of the time value of money. Actually, this idea is one of the core principles of financial mathematics. However, we believe that understanding it is quite simple, even for a beginning in finance.

Let's start with a simple question. Do you prefer to get one hundred dollars today or one hundred dollars after a year from today? If your answer is one hundred today, it means that you intuitively feel the idea of the time value of money. This concept says that one hundred dollars today is worth more than one hundred dollars tomorrow, or, more generally: money that is available now is worth more than the same amount in the future.

Are you wondering why this is? Why is the same amount of money worth more today than in the future? The answer lies in the potential earning capacity of the money that you have now. Note that when you have one hundred dollars from our example, you can put it in your savings account (or make any other investment), and after a year, you will receive more than your initial payment. In fact, it will be one hundred dollars plus additional interest. Formally, economists say that the future value of money is equal to its present value increased by interest. The question that appears here is how to actually calculate this future value of one hundred dollars. Keep reading, and we will try to explain this in details.

Future value definition

By definition future value is the value of a particular asset at a specified date in a future. In other words, future value measures the future amount of money that a given investment is worth after a specified period, assuming a certain rate of return (interest rate). More formally, the future value is the present value multiplied by the accumulation function. This function is defined in terms of time and expresses the ratio of the future value and the initial investment.

Why you need to calculate future value?

It's important to know how to calculate future value if you're a business owner, or indeed any owner of appreciable assets. Once you know how valuable your assets currently are, it's important to know how valuable they will be at any given point in the future. That way, you can plan more intelligently for what's to come. It's important to use a future value calculator in order to get around the problem of the fluctuating value of money. Ultimately, money is our way to assign a number to value. That's why understanding how to calculate the core value of assets, in the present and in the future, is so crucial.

Future value formula

In its simplest version, the future value formula includes the asset's (or the investment) present value, the interest rate, and the number of periods between now and the future date.

Taking into account these variables, you can present the future value equation in the following way:

FV = PV * (1 + r) ^ n

Where:

• FV – future value
• PV – present value (the initial balance of your investment)
• r – interest rate (expressed on an annual basis)
• n – the number of periods (years) the money is invested for.

This formula is applied to investments in which the compounding period is the same as the period for which the interest rate is calculated (e.g., a yearly compounding and an annual growth rate). Sometimes, however, the interest is compounded on a more frequent basis (quarterly or monthly). In such cases to obtain the future value of your investment you need to use a more complex formula:

FV = PV * (1 + r / k) ^ (n * k)

Where:

• k – the compounding frequency (the number of times the interest is compounded per year).

If you don't know all the values in this equation, feel free to use our present value calculator to assess your investment's value at the present moment, and our compound annual growth rate (CAGR) calculator to be sure you plug in the correct interest rate. Usually, the period will be one year as interest rates are often calculated annually.

How to calculate future value? - examples of calculations

Do you want to understand the future value equation? Are you curious how to calculate the future value on real-life examples? Do you need to know how to find the interest rate that will give you a certain profit within a specified period? Or maybe you want to know how much time it will take you to double your initial investment?

We have prepared a few examples to help you find answers to these questions. After studying them carefully, you shouldn't have any trouble with understanding the concept of future value. We also believe that thanks to our examples, you will be able to make smart financial decisions.

Example 1 - Calculating the future value

The first example is the simplest case in which we calculate the future value of an initial investment. Assume that today you make a single deposit of $1,000. The annual interest rate is 4% and it is compounded yearly. What is the future value of this investment after 3 years?

Based on the future value formula presented in the previous section, we can calculate:

FV = $1,000 * (1 + 0,04) ^ 3 = $1,000 * 1,1248 = $1,124.8

The value of your deposit after 3 years (the future value) is $1,124.8.

Let's check now what the future value of the initial amount ($1,000) will be if the annual interest rate is compounded monthly. The formula for future value is:

FV = $1,000 * (1 + 0,04 / 12) ^ (3 * 12) = $1,000 * 1,1273= $1,127.3

This time the future value of your deposit is $1,127.3. Have you noticed that this value is higher (by $2.44) than previously and the only thing that has changed is the compounding frequency? You can say then that the more frequent the compounding, the higher the future value of the investment.

Example 2 - Calculating the present value

In the next example, we will show you how to calculate the present value of any investment. Let's assume that you make a deposit today and want the deposit to grow to $8,000 at the end of 5 years. Knowing that the annual interest rate compounded annually is 3%, calculate the present value of the deposit. In other words, you can ask what amount you need to invest today in order to have $8,000 after 5 years?

The basic transformation of the future value formula allows you to compute the future value:

FV = PV * (1 + r) ^ n

So:

PV = FV / (1 + r) ^ n

PV = $8,000 / (1 + 0,03) ^ 5 = $6,900.87

In our example, if you want to have $8,000 after five years, the initial deposit should be equal to $6,900.87.

Let's consider now what will change if we assume a different compounding period, for example, a quarterly compounding (k = 4).

The respective formula for present value is:

PV = FV / (1 + r / k) ^ (n * k)

So:

PV = $8,000 / (1 + 0,03 / 4) ^ (5 * 4) = $6,889.52

This time the initial deposit should be equal to $6,889.52. Have you noticed that this amount is slightly lower than the previous one? It is the result of the more frequent compounding.

Example 3 - Calculating the number of time periods

In the third example, let's consider another type of question. Firstly, let's assume that you make a simple deposit of $1,000. Like the first example, the annual interest rate is 4%, and it is compounded annually. How many years will it take your deposit to have a future value of $1,200?

To obtain the result, first of all, we need to transform the future value equation in the following way:

FV = PV * (1 + r) ^ n

When both sides are divided by PV:

FV / PV = (1+r) ^ n

So:

log₁₊ᵣ (FV / PV) = n

If the compounding period is not the same as the period for which the interest rate is calculated the formula is:

(log₁₊ᵣ/ₖ (FV / PV)) / k = n

Now, let's try to put values from the example into this formula:

n = log₁,₀₄ (1200 / 1000) = 4,65

It means that it will take 5 annual periods for a $1,000 deposit to go from its present value to the future value of $1200.

What will change if we assume a monthly compounding period? We suggest you try to work it out by yourself. Remember that you can always check your results with our future value calculator – it works in each direction, depending on the values you provide.

Example 4 - Calculating the interest rate

In this example, we present how to calculate the interest rate that is earned on a given investment. The initial balance of todays investment is $15,000. After four years the payoff (future value) from this investment will be $17,000. Assuming that the interest is compounded on an annual basis, what is the yearly interest rate of this investment?

Similarly as in the previous example, let's start with a transformation of the future value formula:

FV = PV * (1 + r) ^ n

Firstly, you need to divide both sides by PV:

FV / PV = (1 + r) ^ n

Then raise both sides to the power of 1 / n

(FV / PV) ^ (1 / n) = 1 + r

The last step is to deduct 1 from both sides:

(FV / PV) ^ (1 / n) – 1 = r

When the compounding period is not the same as the period for which the interest rate is calculated:

((FV / PV) ^ (1 / n * k) – 1) * k = r

So the solution of our example is as follows:

r = (17,000 / 15,000) ^ (1 / 4) – 1 = 3.18%

The yearly interest rate in the considered investment is then 3.18%.

Try to calculate the annual interest rate on this investment if interest is compounded monthly. Is this interest rate higher or lower than interest rate from the example? What is the reason for that? Once again, in case you are not sure about your results, feel free to use our calculator – it is able to compute the interest rate based on the other information that you provide.

How to use the future value calculator?

Now, when you know how to compute the future value, you can try to make your calculations faster and simpler with our future value calculator. This calculator is a tool for everyone who wants to make smart and quick investment calculations. It is also highly recommended for any investors, from shopkeepers to stockbrokers.

With our calculator obtaining the future value of your investment is easier than you thought. To compute the future value of your investment you don't need to memorize any formulas or perform any calculations. All you need to do is to fill in the appropriate fields on our calculator:

• present value – type in the amount of money you are going to invest (it's the initial deposit)
• interest rate – provide the interest rate on your investment expressed on a yearly basis
• period – here you should type in the number of years you are going to invest money (it's the period of investment)
• compound frequency – select the compounding frequency. Usually, the interest is calculated daily, weekly, monthly, quarterly, half-yearly or yearly

That's it! In less than a second, our calculator makes every computation and displays the results. They are shown in the future value field, where you should see the future value of your investment.

Did you know that you can also use the future value calculator the other way round? For example plug in the present value, the future value and the interest rate to find how long you need to invest to get the provided future value.

In conclusion, future value calculator helps you make smart financial decisions. With the mobile version of our application, you are also able to use our FV calculator wherever and whenever you want.

How to double your money? – the rule of 72

The Rule of 72 tells you how much time it takes for something to double given a certain level of constant growth rate. This rule is a simple technique that allows you to estimate quickly:

• the time it takes your initial deposit to double when you know the interest rate or
• the interest rate you need to double your initial deposit within a specified period.

The Rule of 72 says that the deposit will double when

r * n = 72.

where:

• r – interest rate per period (year)
• n – the number of periods (years)

For example, the Rule of 72 states that your initial deposit earning 6% per year compounded annually will double in 12 years. We know it from the following equation:

6% * n = 72

So:

n = 72 / 6 = 12

From another point of view, the Rule of 72 indicates that, to double the investment in 6 years, it should earn 12% per year, compounded annually:

r * 4 = 72

So:

r = 72 / 6 = 12

You can find more details and interesting information about the Rule of 72 at our original rule of 72 calculator.

Other important financial calculators

Future value calculations are closely tied to other financial mathematic formulas. We applied most of them in our incredible Omni calculators. Below you will find some of them:

• Very helpful in comparing bank offers with different compounding periods, is the APY calculator, which estimates the Annual Percentage Yield from the interest rate and compounding frequency.
• If you want to estimate the average yearly gain from your investment, you should use the CAGR calculator.
• You may be interested in the credit card payoff calculator which allows you to estimate how long it will be until you are completely debt-free.
• Another interesting calculator is our cap rate calculator which determines the rate of return on your real estate property purchase.
• The dream come true answers the question: how long do you have to save to afford your dream?
• The NPV calculator gives you information on the present value of future cash flows.
• If you have set of incoming cash flows (a.k.a. an annuity) that you are expecting click through to our future value of annuity calculator to learn more.

Tomasz Jedynak, PhD, Piotr Małek and Mateusz Mucha

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