Future Value Calculator
Future Value Formula
- Present Value of Investment (PV): The amount of money invested at the starting period.
- Interest Rate (r): The expected annual rate of return, explained in more detail below.
- Number of Years (t): The number of years you want to hold the investment.
- Compounding Frequency (n): How many times per year the investment compounds.
Calculating future value allows you to predict how much an investment will be worth. The concept is based on the time value of money, which believes that $1 today is more valuable than $1 in two years. This is because the dollar today can be invested and earn compound interest. As a result, assets should become more valuable in the future.
The formula is often used during tax planning to calculate capital gains tax that must be paid upon selling. Individual investors also use it during retirement planning to predict the size of their future net worth.
To calculate the future value, you will need to know four variables. These factors include the initial amount invested, the interest rate, investment time, and compounding frequency. Together, these form the future value calculation shown above.
Tip: Time Value of Money Explained
Time value of money is based on the idea that assets should be worth more than they are right now. That's because if you have $1 today, you can invest it and make more money over time. Calculating future value allows you to estimate your money's worth at a future date, assuming you invest it at an estimated interest rate.
The Types of Future Value Calculations
While the formula mentioned above is the standard future value calculation, in reality, there are many. For example, your formula will change depending on your payment frequency.
- Lump Sum: A one-time payment that is left untouched.
- Annuity: Frequent payments that are contributed at a specific frequency.
- Hybrid: A combination of a one-time payment with additional payments.
Future Value of a Lump-Sum
A lump sum is a one-time payment. For example, you invest $10,000 in a certificate of deposit (CD) and leave it for five years. A lump sum doesn't include recurring payments. However, if there are a few recurring payments, you can treat them as individual lump sums and then add the total future value.
The future value of a lump-sum investment is calculated by multiplying the initial amount invested by the future value factor. For example, assume you invest $10,000 today at an annual rate of 6.00% with semi-annual compounding. You plan to sell the investment in five years and want to predict the future value. As a result, your inputs are:
- Present Value (PV): $10,000
- Interest Rate (r): 6.00%
- Number of Years (t): 5
- Compounding Frequency (n): two times per year
These would translate to the following equation
Lump-Sum Future Value Calculation
Therefore, after five years your investment would be worth $13,439.16.
Future Value of an Annuity
An annuity is a frequently recurring payment. For example, you invest $500 in a CD every six months for five years. In most cases, the annuity formula assumes the payment sizes remain the same. However, there are more complex formulas to calculate changing payments. While our calculator doesn't feature the future value of an annuity, the formula is below:
Annuity Future Value Formula
- Recurring Payment (PMT): The recurring payment at the designated frequency.
- Interest Rate (r): The anticipated annual rate of return.
- Number of Years (t): The number of years you want to keep the investment.
- Compounding Frequency (n): How often per year the investment compounds.
Calculating an annuity's future value is done by multiplying the recurring payment by an annuity factor. Let's take our example from earlier and assume you invest $1,000 at the end of every year. You have no savings now, so you must wait until the end of this year to invest. Your contributions earn a 6.00% interest rate and compound semi-annually. Your inputs would equate to the following:
- Recurring Payment (PMT): $1,000
- Interest Rate (r): 6.00%
- Number of Years (t): 5
- Compounding Frequency (n): Two times per year
You would then use the following calculation:
Example Annuity Future Value Calculation
Therefore, after five years of semi-annual payments, your investment would be worth $11,463.88.
In many cases, you make an initial lump-sum investment with frequent contributions. In this scenario, you would combine lump sum and annuity calculations. After calculating the future values for both options, you would sum them at the final period to calculate the closing balance.
Future Value Calculator Explained
The calculator is used to find the future value of a lump sum in the desired year. You must enter the initial amount, interest rate, compounding frequency, and selected period. The calculator will then automatically calculate your future value based on these inputs. Your future value will change by altering the following information:
- Increasing present value increases future value because you start with a higher amount.
- Increasing the rate of return increases the future value because you receive a higher ROI.
- Increasing the compounding frequency increases future value because more interest is earned over a shorter period.
- Decreasing the investment time decreases future value because more interest there is less time for your money to grow.
After inputting the relevant information, our calculator will provide you with an estimate of the lump-sum amount's future value in the desired year.
Determining The Interest Rate
|Historical Annualized Return|
The risk-free rate is the minimum interest rate you should accept. This is because it's the return on investment you could receive with no risk. Typically, the rate is the 10-year treasury yield. The treasury yield is backed by the United States government, which implies no default risk. As a result, investing in a lower interest rate doesn't make sense if you can receive a higher treasury rate without risk. Currently, the risk-free rate is 3.781%.
Market Rate of Return
The market rate of return is the average interest rate you can expect from investing in a specific asset class or investment type. This is determined by analyzing historical rates of return for different investments.
For example, the market rate would be based on the average stock market returns over time if you are looking to invest in stocks. Similarly, if you are looking to invest in bonds or real estate, then the market rates would be based on historical returns for those asset classes.
However, you should carefully evaluate each investment's risks and potential returns before deciding which one is right for you. The table above takes selected information from our U.S. inflation calculator to see historical asset performance.
The Bottom Line
Ultimately, the future value estimates how much your investment will be worth at a future date. To calculate it, you'll need to know your initial investment, interest rate, holding period, and compounding frequency. An annuity formula is better for you if you wish to make frequent contributions. However, if you're making a one-time payment, you'll only need the lump-sum formula. Finally, your estimated interest rate should exceed the risk-free rate and can be derived from historical asset performances.