What is the future value formula?

For an ordinary annuity with an initial principal, FV = PV * (1 + r)^n + PMT * ((1 + r)^n - 1) / r, where PV is present value, PMT is periodic payment, r is rate per period, and n is number of periods.

What is the difference between an ordinary annuity and an annuity due?

In an ordinary annuity, payments occur at the end of each period. In an annuity due, payments occur at the beginning of each period, earning an extra period of compounding interest.

How does this compare to Excel's FV function?

Excel uses =FV(rate, nper, pmt, [pv], [type]). Note that Excel assumes cash flow signs: outgoing cash flows are entered as negative numbers to return a positive future value.

Future Value Calculator

Determine the future value of a lump sum investment or regular periodic savings.

Formula:

FV = PV × (1 + r)ⁿ + PMT × ((1 + r)ⁿ − 1) / r (for r > 0)
FV = PV + PMT × n (when r = 0)
Standard ordinary annuity formula: payments are made at the end of each period.

How future value works

The intuition

Future Value (FV) calculates what a sum of money invested today — or a stream of recurring deposits — will grow to after compounding at a given interest rate over a set number of periods. Because interest generates its own interest over time, exponential growth accelerates your total wealth.

Ordinary annuity vs. annuity due

This calculator computes an ordinary annuity, where recurring deposits happen at the end of each period (standard for most retirement accounts and savings plans). In contrast, an annuity due deposits money at the beginning of each period, multiplying the annuity component by (1 + r).

Using Excel or a TI-84 calculator

In Microsoft Excel or Google Sheets, the corresponding formula is =FV(rate, nper, pmt, [pv], [type]). Because financial spreadsheets follow cash-flow accounting conventions (cash outflows are negative), enter deposits as negative values to get a positive future balance: =FV(5%, 10, -100, -1000, 0) gives 2886.68. On a TI-84 financial solver, enter N=10, I%=5, PV=-1000, PMT=-100, and solve for FV.

Worked examples

Example 1: Lump sum $1,000 at 5% for 10 periods (PMT = 0)

Enter PV = 1000, PMT = 0, rate = 5, periods = 10. The lump sum grows to $1,628.89 (1628.89).

Example 2: Pure annuity of $100/period for 10 periods at 5% (PV = 0)

Enter PV = 0, PMT = 100, rate = 5, periods = 10. The accumulated annuity equals $1,257.79 (1257.79).

Example 3: Combined principal and annuity at 5% for 10 periods

Enter PV = 1000, PMT = 100, rate = 5, periods = 10. The total future value combines both parts to reach $2,886.68 (2886.68).

Related tools

Future value is the direct counterpart of the Present Value Calculator, which discounts a future sum back to today's dollars.

Multi-decade growth tracking. For visual balance accumulation and interest breakdowns over decades, see our calculator for compound interest growth.
Reverse calculations. If you already know your target balance and want to solve for the monthly contribution needed, use the Savings Goal Calculator.
Cash flow series. For uneven streams of cash inflows and outflows, calculate net value with the NPV / IRR Calculator.
Borrowing and amortization. To model amortized debt repayment rather than accumulation, use the Loan Calculator.

Frequently asked questions

Can I calculate future value if interest rate is 0%?

Yes. When the rate is 0%, no compounding occurs and the formula simplifies to FV = PV + PMT × n. For example, $1,000 principal plus 10 deposits of $100 equals $2,000.

How do I input annual vs. monthly periods?

Ensure that the interest rate matches the frequency of your periods. If deposits are monthly for 10 years (120 periods), divide your annual interest rate by 12 (e.g. 6% annual becomes 0.5% per month).

Does this result account for inflation or taxes?

No. The calculation provides a nominal, pre-tax value. To estimate purchasing power in real terms, adjust the interest rate downwards by the expected inflation rate.