Future Value of an Annuity Calculator
Introduction to Future Value of an Annuity
An annuity, as used here, is a series of regular, periodic payments to or withdrawals from an investment account. Wikipedia lists the following examples of annuities: “regular deposits to a savings account, monthly home mortgage payments, monthly insurance payments, and pension payments.” Annuities can be classified by the frequency of the cash-flow dates. The investor may make deposits (or withdrawals or payments) weekly, monthly, quarterly, yearly, or at any other regular interval. This calculator supports eleven frequency options.
The Accurate Future Value of an Annuity Calculator calculates the FV of a series of periodic amounts.
- Create printable schedules with dates
- Export or print charts
"What will be the final value of a series of deposits, withdrawals or investments?"
The future value of an annuity is the total amount the cash flow will be worth on a future date. Because the account earns investment gains or interest on the principal, the final value is greater than the sum of the deposits.
This future value of an annuity (FVA) calculator computes the value on any specified future date. You may enter a starting amount that differs from the periodic deposit. This allows you to calculate the FVA of an existing investment.
If the investment is new, set “Starting Amount (PV)” to 0.
This FVA calculator can also calculate the future value after a series of withdrawals. For example, if you start with $1,000,000 and assume it earns 4.0% per year, the calculator will compute the value after 30 years of monthly withdrawals of $5,000. To indicate a withdrawal, enter a negative amount.
Future Value of an Annuity-calculate the value of a series of investments or deposits
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Instructions for the Future Value of an Annuity Calculator
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- Starting Amount (PV): The money you have at the beginning of the annuity period. It may be the initial investment or the current value of an existing annuity.
- Periodic Amount: The amount of money you will withdraw (negative value) or contribute (positive value) at regular intervals. The annuity terms determine both the amount and the frequency.
- Number of Periods: The number of times the periodic cash flow will occur.
- Annual Interest Rate: The yearly interest rate the annuity will earn, expressed as a percentage.
- Start Date: The present value date (see note below). This may be the date you purchase the annuity or another predetermined date.
- First Contribution Date: The date of the first contribution (or withdrawal) from the annuity. This may be the same as the start date or a later date.
- Cash Flow Frequency: How often you will contribute to or withdraw from the annuity. Examples: monthly, quarterly, annually, or another interval.
- Monthly Compounding: How often the interest on the annuity is compounded. If you are unsure of the compounding frequency, set it to match the cash flow frequency.
Note: An annuity is a regular cash flow—either scheduled contributions or withdrawals. Because this calculator lets the user specify both a start date and a first cash flow date that may not match, it can calculate the future value accurately. This remains true even if the cash flows do not begin until years later.
Future Value of an Annuity Equations
In this section:
Future Value of an Ordinary Annuity Equation (with a starting amount)
For an ordinary annuity, the cash flows occur at the end of each period. To model this, set “First Contribution Date” to any date after “Start Date.” The calculator supports a stub (irregular-length) first period, although the equation itself does not.
Fig. 2 – Step-by-step solution of the Future Value of an Ordinary Annuity Equation.
Variables: PV = 32,500; PMT = 525; R = 7.5%; n = 48; f = 12.
Variable Definitions
- R
- Nominal annual interest rate.
- f
- Number of compounding periods per year.
- i
- Periodic interest rate.
- PV
- Present Value—the starting amount (may be 0).
- PMT
- Periodic cash flow amount. All cash flows are equal.
- n
- Total number of cash flows.
Calculation Steps Explained – Fig. 2
- How do you calculate the future value of an ordinary annuity with a starting amount?
To calculate the future value of an ordinary annuity with a present value (starting amount), use a compound interest equation that accounts for both the initial lump sum and a series of equal payments made at the end of each period. The process is as follows, using these inputs:
PV = 32,500,PMT = 525,n = 48months,R = 7.5%annual interest rate, andf = 12compounding periods per year.- Calculate the periodic interest rate by dividing the nominal annual rate by the number of compounding periods per year:
i = R ÷ f = 0.075 ÷ 12 = 0.00625. - Add 1 to the periodic rate:
1 + i = 1.00625. - Raise the base to the power of the total number of periods:
(1.00625)48 ≈ 1.34859915. - Substitute values into the future value equation:
FV = PV × (1.00625)48 + PMT × [(1.00625)48 − 1] ÷ 0.00625. - Evaluate each part:
32,500 × 1.34859915 ≈ 43,829.47;525 × 55.77586421 ≈ 29,282.33. - Add both parts to calculate the future value:
43,829.47 + 29,282.33 = 73,111.80.
An initial deposit of $32,500 plus 48 monthly payments of $525, invested at a 7.5% annual interest rate compounded monthly, will grow to approximately $73,111.80 at the end of the investment period.
- Calculate the periodic interest rate by dividing the nominal annual rate by the number of compounding periods per year:
Step-by-step Solution – Fig. 2
FV = 32,500 × (1.00625)48 + 525 × [(1.00625)48 − 1] ÷ 0.00625≈ 32,500 × 1.34859915 + 525 × (0.34859915 ÷ 0.00625)≈ 32,500 × 1.34859915 + 525 × 55.77586421≈ 43,829.47 + 29,282.33≈ 73,111.80
Final Answer
The final answer (FV) is approximately 73,111.80.
Validate the calculator. Inputs for a 48 months future value schedule.
| Starting Amount (PV): | 32,500.00 | Periodic Amount (+/−): | 525.00 |
|---|---|---|---|
| Number of Periods: | 48 | Annual Interest Rate: | 7.5% |
| Start Date: | First Contribution Date: | ||
| Cash Flow Frequency: | Monthly | Compounding: | Monthly |
| No./Year | Date | Investment | Interest | Net Change | Balance/FV |
|---|---|---|---|---|---|
| 47:4 | 525.00 | 444.79 | 969.79 | 72,135.97 | |
| 48:4 | 525.00 | 450.85 | 975.85 | 73,111.82 | |
| 2029 YTD: | 4,200.00 | 3,439.18 | 7,639.18 | ||
| Running Totals: | 57,700.00 | 15,411.82 | |||
| The future value is $0.02 higher than the equation result because the schedule rounds intermediate interest to two decimal places. | |||||
Notes:
- This example uses the same calculation shown in Fig. 2.
- If you run this example in the calculator, the future value will be 73,111.82. The difference occurs because the calculator generates a monthly schedule and rounds each interest amount to two decimal places. The closed-form equation does not round intermediate values.
- The starting amount may be 0.
Future Value of an Annuity Due Equation (with a starting amount)
For an annuity due, the cash flows occur at the beginning of each period. To model this, set “First Contribution Date” equal to “Start Date.”
Fig. 4 – Step-by-step solution of the Future Value of an Annuity Due Equation.
Variables: PV = 32,500; PMT = 525; R = 7.5%; n = 48; f = 12.
Variable Definitions
- R
- Nominal annual interest rate.
- f
- Number of compounding periods per year.
- i
- Periodic interest rate.
- PV
- Present Value—the starting amount (may be 0).
- PMT
- Periodic cash flow amount. All cash flows are equal.
- n
- Total number of cash flows.
Calculation Steps Explained – Fig. 4
- How do you calculate the future value of an annuity due with a starting amount?
The calculation combines the growth of the initial lump sum with the growth of the annuity-due cash flow stream. The periodic rate is derived from the nominal annual interest rate (APR) and the compounding frequency. Values are then substituted into the equation and simplified step by step. Approximations are indicated by ellipses.
- Calculate the periodic rate from the nominal APR and compounding frequency:
i = R ÷ f = 0.075 ÷ 12. - Evaluate the periodic rate:
i = 0.00625. - Substitute into the combined future value equation (lump sum plus annuity due):
FV = (32,500 + 525) × (1 + 0.00625)48 + 525 × [((1 + 0.00625)48 − 1 − 1) ÷ 0.00625] × (1 + 0.00625). - Simplify the base while retaining the exponent form:
FV = 33,025 × (1.00625)48 + 525 × [((1.00625)48 − 1 − 1) ÷ 0.00625] × (1.00625). - Approximate the growth factors:
(1.00625)48 ≈ 1.34859915…and(1.00625)47 ≈ 1.34022276…. Update the bracket:FV ≈ 33,025 × 1.34859915… + 525 × [(1.34022276… − 1) ÷ 0.00625] × 1.00625. - Simplify inside the bracket:
FV ≈ 33,025 × 1.34859915… + 525 × (0.34022276… ÷ 0.00625) × 1.00625. - Divide the bracket and retain the timing multiplier:
FV ≈ 33,025 × 1.34859915… + 525 × 54.43564146… × 1.00625. - Compute the lump-sum product and carry the annuity factor:
FV ≈ 44,537.49… + 525 × 54.77586421…. - Multiply the periodic payment by the adjusted factor:
FV ≈ 44,537.49… + 28,757.33…. - Add both parts and round to two decimals:
FV ≈ 73,294.82.
This procedure grows the initial lump sum for all periods and adds the annuity-due cash flow stream with the beginning-of-period timing adjustment.
- Calculate the periodic rate from the nominal APR and compounding frequency:
Step-by-step Solution – Fig. 4
i = 0.075 ÷ 12= 0.00625FV = (32,500 + 525) × (1 + 0.00625)48 + 525 × [((1 + 0.00625)48 − 1 − 1) ÷ 0.00625] × (1 + 0.00625)= 33,025 × (1.00625)48 + 525 × [((1.00625)48 − 1 − 1) ÷ 0.00625] × (1.00625)≈ 33,025 × 1.34859915… + 525 × [(1.34022276… − 1) ÷ 0.00625] × 1.00625≈ 33,025 × 1.34859915… + 525 × (0.34022276… ÷ 0.00625) × 1.00625≈ 33,025 × 1.34859915… + 525 × 54.43564146… × 1.00625≈ 44,537.486973… + 525 × 54.77586421…≈ 44,537.49… + 28,757.33…≈ 73,294.82
Final Answer
The final answer (FV) is approximately 73,294.82 at the end of the 48th period.
Notes:
- For an annuity due, the calculator’s schedule stops at the beginning of the final period. As a result, the schedule output will be less than the equation result by the amount of interest earned during that final period. This behavior may change in a future update.
- The starting amount may be 0.
Future Value of an Annuity Calculator Help
Money in any form—cash, investments, receivables, and so on—has a different value tomorrow, next month, or next year than it does today. Even money kept as cash without earning interest will have less value in the future than it does today. This change in value is called the “future value.”
You must enter either a “Starting Amount” (the amount of cash on hand), a “Regular Contribution Amount”, or both. Set how often you add to your investment by selecting the “Contribution Frequency.” For example, if you set the contribution frequency to monthly and enter 120 for “Number of Contributions”, then the “Future Value” will be calculated for the date that is 10 years from the “First Contribution Date” (120 monthly contributions = 10 years).
Compounding Frequency: Selecting the “Exact/Simple” option means the calculator does not compound the interest. Instead, it calculates interest for each period using the exact number of days between withdrawal dates. The “Daily” option also uses the exact number of days between dates, but it assumes daily compounding (interest earned each day is added to the principal each day). The “Exact/Simple” setting is the most conservative option, producing the lowest future value. Daily compounding produces a higher future value (close to the maximum, except for “Continuous Compounding”).
The other compounding frequencies are based on periods longer than one day. Each period is treated as equal in length for interest calculations. For example, if the balance is $10,000, then the interest earned for January will equal the interest earned for February, given the same annual interest rate.
Note: The future value may be lower than today’s value if inflation is considered. To reflect this, enter a negative interest rate.
W S Beckwith says:
Very nice tool. Just wish you had the capability to show negative values in your Balance/FV column. Thanks!
Karl says:
Thanks for the compliment.
Here’s another calculator – the Ultimate Financial Calculator that will probably do what you want (I say probably because I’m not sure what you need besides the negative balance.
If you try it, scroll down the page and you’ll there’s a number of tutorials.
Assuming you have some amount call it "X", and you want to make withdrawals, set the Schedule Type to "savings". Create two rows, the first row as a deposit with value "X" and the second row with value "Y" for the number of withdrawals you expect. If Rounding (under settings) is set to "Open Balance", the balance will go negative.
Let me know if there are other details, and I’m sure we can work through them.
sal says:
Hi,
The Future Value calculator is not calculating values. It only shows 4 months of data even if the selection is more than 4 month period. Can someone look into this. This is a great tool that provides future projected cash values. Really love it. Hoping to get this fixed.
Karl says:
Hello, That’s really embarrassing.
I recently made a small change that broke some calculators. This morning I released a fix.
Please try again.
If you do not see the change right away, you may have to perform a hard refresh of the page:
Depending on your operating system all you need to do is the following key combination:
Above, from Refresh Your Cache.
If you don’t mind, please let me know if the problem is resolved for you.
Thanks!
sal says:
Hi,
Yes the problem is resolved. I appreciate the quick fix.
Thank you so much
Karl says:
You’re welcome. Thanks for the confirmation.
sumit thakur says:
Is it Available on WordPress widget?
Karl says:
This calculator is not available as a plugin. However, the FC Savings Calculator Plugin is very similar. Perhaps it will meet your needs?
Tim Chapman says:
I have a sum invested and I would like to know how much I can draw from that sum every month whilst keeping the inflation adjusted value of the sum the same.
Another way of putting this is my monthly withdrawal should equate to the interest on the sum minus the adjustment for inflation.
Is it as simple as subtracting the monthly rate of inflation from the monthly rate of growth and applying that to the sum invested to get my monthly withdrawal amount?
Karl says:
The Ultimate Financial Calculator is designed for this problem.
Change "Schedule Type" to "Savings."
Click on "Cash Flow Options" for your withdrawal series and select "Percent Step."
Enter the assumed inflation rate as the "Percent change per level."
If you have any questions, please ask them Also note the link on the above page to a number of different tutorials.