What is the future value?
Enter a starting amount, a payment each period, the yearly rate, how often it compounds, and the years. See the future value and the interest.
- Future value
- $19,226.56
At 6% a year for 10 years, $11,000.00 put in grows to a future value of $19,226.56.
- Money put in
- $11,000.00
- Interest
- $8,226.56
- Future value of the starting amount
- $17,908.48
- Future value of the payments
- $1,318.08
- Number of periods
- 10
- Years
- 10
Future value: $19,226.56. At 6% a year for 10 years, $11,000.00 put in grows to a future value of $19,226.56.
How much of it is interest?
How does it grow?
What does each year look like?
The results are estimates for information only. They are not financial, tax, or legal advice. Check the numbers with your lender or a qualified professional before you decide. Terms of use
How to calculate
Computes the future value of a present amount plus a level payment each period, at a yearly rate compounded 1, 2, 4, or 12 times a year, with payments at the start or end of each period.
Example with the default inputs (Starting amount (present value) $10,000.00, Payment each period $100.00, Yearly interest rate 6%, Periods a year Yearly, Number of years 10, Payments are made at the End of each period): At 6% a year for 10 years, $11,000.00 put in grows to a future value of $19,226.56.
Method: FV = PV × (1 + r)^n + PMT × ((1 + r)^n − 1) ÷ r, times (1 + r) on the payments when they are made at the start of each period, with r = yearly rate ÷ periods a year and n = years × periods a year; worked period by period.
- The rate stays the same for every period, and interest is added once per period.
- All payments are the same size, one per period.
- No fees or taxes are taken out.
- This is an estimate for planning, not financial advice.
Worked examples
Each example is checked against the calculator on every build.
- Starting amount (present value) $1,000.00, Yearly interest rate 5%, Periods a year Yearly, Number of years 10, Payments are made at the End of each period gives Future value $1,628.89, Interest $628.89, Future value of the starting amount $1,628.89.Source: FV = PV × (1 + r)^n, hand calculation in content.mdx
- Starting amount (present value) $0.00, Payment each period $100.00, Yearly interest rate 6%, Periods a year Yearly, Number of years 10, Payments are made at the End of each period gives Future value $1,318.08, Money put in $1,000.00, Future value of the starting amount $0.00, Future value of the payments $1,318.08.Source: future value of an ordinary annuity, PMT × ((1 + r)^n − 1) ÷ r; hand calculation in content.mdx
- Starting amount (present value) $0.00, Payment each period $100.00, Yearly interest rate 6%, Periods a year Yearly, Number of years 10, Payments are made at the Start of each period gives Future value $1,397.16.Source: future value of an annuity due, times (1 + r); hand calculation in content.mdx
- Starting amount (present value) $0.00, Payment each period $100.00, Yearly interest rate 6%, Periods a year Monthly, Number of years 10, Payments are made at the End of each period gives Future value $16,387.93, Number of periods 120.Source: monthly: r = 0.5%, n = 120, 100 × (1.005^120 − 1) ÷ 0.005; hand calculation in content.mdx
- Starting amount (present value) $1,000.00, Payment each period $100.00, Yearly interest rate 0%, Periods a year Yearly, Number of years 12, Payments are made at the End of each period gives Future value $2,200.00, Interest $0.00.Source: hand calculation in content.mdx: 1,000 + 12 × 100
How the future value is worked out
The yearly rate is split into periods: with f periods a year (1, 2, 4, or 12), the rate per period is r = yearly rate ÷ f (as a decimal), and there are n = years × f periods. Interest is added and one payment is made every period. With a starting amount PV and a payment PMT each period:
FV = PV × (1 + r)^n + PMT × ((1 + r)^n − 1) ÷ r
When payments are made at the start of each period (an annuity due), the payment part is multiplied by (1 + r). When r is 0, FV = PV + PMT × n. An empty payment counts as $0.
The calculator also works it out period by period, and shows one row per year:
- Payment at the start: interest = (balance + payment) × r.
- Payment at the end: interest = balance × r.
- The new balance is balance + payment + interest.
The results:
- Future value is the balance after the last period.
- Money put in is PV + PMT × n. Interest is the future value minus the money put in.
- Future value of the starting amount is PV × (1 + r)^n. Future value of the payments is PMT × ((1 + r)^n − 1) ÷ r (times (1 + r) for payments at the start, PMT × n at 0%), and exactly $0 with no payment.
- Number of periods is n = years × f.
Assumptions
- The rate is the same in every period, and interest is added once per period.
- No fees or taxes are taken out.
- This is an estimate for planning, not financial advice.
Worked examples by hand
$1,000 at 5% a year, yearly, for 10 years. FV = 1,000 × 1.05^10 = 1,000 × 1.628895 = $1,628.89, so the interest is $628.89.
$100 at the end of each year at 6% for 10 years. 1.06^10 = 1.790848. FV = 100 × (1.790848 − 1) ÷ 0.06 = 100 × 13.18079 = $1,318.08. The money put in is 10 × 100 = $1,000.
The same payments at the start of each year. FV = 1,318.08 × 1.06 = $1,397.16.
$100 at the end of each month at 6% a year for 10 years. r = 0.06 ÷ 12 = 0.005 and n = 120. 1.005^120 = 1.819397. FV = 100 × 0.819397 ÷ 0.005 = 100 × 163.8793 = $16,387.93.
$1,000 plus $100 a year at 0% for 12 years. FV = 1,000 + 12 × 100 = $2,200, with no interest.
Other questions people ask
What is future value?
Future value (FV) is what an amount of money today, plus any regular payments, will be worth at a later date when it earns interest. $1,000 at 5% a year is worth $1,628.89 after 10 years.
What is the future value formula?
For a single amount: FV = PV × (1 + r)^n, where PV is the amount today, r the rate per period, and n the number of periods. For a level payment PMT at the end of each period, add PMT × ((1 + r)^n − 1) ÷ r. When payments are at the start of each period, multiply that payment part by (1 + r).
What is the difference between an ordinary annuity and an annuity due?
In an ordinary annuity each payment is made at the end of the period. In an annuity due it is made at the start, so every payment earns one more period of interest and the future value is (1 + r) times larger. $100 a year for 10 years at 6% grows to $1,318.08 as an ordinary annuity and $1,397.16 as an annuity due.
How do I use monthly payments?
Pick "Monthly" under periods a year. The rate per period is then the yearly rate ÷ 12 (6% a year is 0.5% a month), and there are 12 periods each year. $100 a month for 10 years at 6% grows to $16,387.93. If your rate is an effective yearly return instead, the monthly rate would be 1.06^(1/12) − 1 = 0.4868%.
How is future value different from present value?
They are the same equation read in opposite directions. Future value moves money forward in time by multiplying by (1 + r)^n. Present value moves it back by dividing by (1 + r)^n: $1,628.89 in 10 years at 5% is worth $1,000 today.