The future value formula calculates how much one amount today will become after earning a periodic rate for a set number of periods. Multiply present value by one plus the periodic rate raised to the number of compounding periods.
FV = PV × (1 + i)^n
— value at the chosen future date
— single amount invested, borrowed, or valued at the starting date
— growth or interest rate per compounding period, as a decimal
— total number of compounding periods
FV = PV × (1 + r_nom / m)^(m × t)
— nominal annual rate, as a decimal
— number of compounding periods per year
— investment or loan term in years
— starting and ending value of the same lump sum
PV is the starting lump sum. If $13,750 is deposited today, PV is $13,750. The basic formula assumes no additional deposits or withdrawals. Regular contributions create a series of cash flows and require an annuity formula or separate future-value calculation for each contribution.
i is the rate for one compounding period. When a nominal annual rate is compounded quarterly, divide it by four to obtain the rate per quarter. A 6.2% nominal annual rate becomes 1.55% per quarter, or 0.0155. If the rate supplied is already an effective annual rate and you need a quarterly rate, take an equivalent quarterly root instead of simply dividing by four.
n is the number of periods that earn interest. Seven years with quarterly compounding gives 28 quarters. Rate and period count must share the same unit. If i is quarterly, n counts quarters; if i is monthly, n counts months.
The exponent creates compound growth. After the first period, interest is added to principal. The next period earns a return on both the original balance and the earlier interest. Repeating that multiplication produces a curved growth path rather than the straight-line growth of simple interest.
The expression raised to n is a future-value factor. It tells you how many dollars the investment has at the end for each dollar at the beginning. A factor of 1.5383 means each starting dollar becomes about $1.5383 under the stated rate and time assumptions.
| Point | Calculation or balance | Value |
|---|---|---|
| Starting principal | PV | $13,750.00 |
| Quarterly rate | 6.2% / 4 | 1.55% |
| Total periods | 7 years × 4 | 28 quarters |
| End of year 1 | $13,750 × (1.0155)^4 | $14,622.53 |
| End of year 2 | $13,750 × (1.0155)^8 | $15,550.42 |
| End of year 3 | $13,750 × (1.0155)^12 | $16,537.19 |
| End of year 4 | $13,750 × (1.0155)^16 | $17,586.59 |
| End of year 5 | $13,750 × (1.0155)^20 | $18,702.57 |
| End of year 6 | $13,750 × (1.0155)^24 | $19,889.37 |
| End of year 7 | $13,750 × (1.0155)^28 | $21,151.48 |
The future value is $21,151.48. Subtracting the $13,750 opening principal shows total accumulated interest of $7,401.48. The interest earned each year grows because the balance that earns the next year's return includes earlier interest.
The year-by-year rows are also an audit trail. At the end of year 1, four quarterly periods have elapsed; at the end of year 7, 28 have elapsed. A result based on only seven applications of 1.55% would understate the ending balance because it would model seven quarters rather than seven years.
Future value includes both the original principal and accumulated interest. Compound interest earned is the difference between future value and present value when there are no intervening cash flows. This explains why some sources show a compound-interest expression with a subtraction: they are solving only for interest, while the future-value formula solves for the full ending balance.
Simple interest uses the opening principal as the interest base in every period. Compound interest updates the base after interest is credited. For one period, both approaches give the same result at the same rate. Over multiple periods, positive compound growth produces a higher value because interest itself begins earning interest.
Holding a positive nominal annual rate constant, more frequent compounding raises future value because interest is credited sooner. The increase becomes smaller as frequency rises. Be careful about comparing products from the nominal rate alone: convert each quote to an effective annual rate or calculate each future value using its own compounding terms.
The displayed rate must be interpreted correctly. A phrase such as “6.2% compounded quarterly” usually identifies a nominal annual rate allocated across four quarters. A phrase such as “6.2% effective annually” already gives the one-year growth rate. The two statements do not imply identical quarterly rates.
The lump-sum formula follows one deposit from start to finish. If you deposit $500 at the end of every month, the first $500 compounds longer than the last. Do not add all contributions to the starting PV and compound the total for the entire horizon; that gives late deposits interest they never earned. Use a future-value-of-annuity method for equal periodic deposits, or compound each uneven contribution for its actual remaining periods.
Beginning-of-period contributions also differ from end-of-period contributions. A deposit made at the start of each month earns one additional month compared with the same deposit made at month-end. A timeline makes that distinction visible before you choose a formula or spreadsheet setting.
Using an annual rate with a quarterly exponent. Convert the annual quote to a rate per quarter before using 28 quarters.
Using years for n after converting i to monthly or quarterly. Once i changes units, n must change with it. Write the unit beside each number.
Entering 6.2 instead of 0.062. Convert percentages to decimals before arithmetic, then report the final growth rate or return as a percentage when needed.
Adding contributions to PV as if they were invested on day one. Separate cash flows by deposit date or use the appropriate annuity formula.
Calling FV the interest earned. FV is the ending balance. Subtract starting principal to isolate accumulated interest when no other cash flows occur.
Rounding every checkpoint. The annual balances are useful displays, but the final answer should be calculated from full precision rather than from rounded year-end values.
Excel and Google Sheets use FV(rate, nper, pmt, [pv], [type]). For the lump-sum example, enter a quarterly rate of 1.55%, 28 periods, zero periodic payment, and a present value of -13750. The negative sign reflects the cash-flow convention and returns a positive ending value. When contributions exist, use the pmt argument and set type to 0 for period-end deposits or 1 for period-beginning deposits.
Future value compounds one starting amount forward. Match the rate to the compounding period, count those periods over the full horizon, and keep later contributions separate from money invested at the start.
Multiply the present lump sum by one plus the periodic interest rate raised to the total number of compounding periods. The rate and period count must use the same time unit.
Future value moves a cash flow forward through compounding. Present value moves a future cash flow backward through discounting. They are inverse calculations when the rate and dates match.
Future value is the full ending balance, including principal. Compound interest earned is future value minus starting principal when there are no other deposits or withdrawals.
Use the monthly rate and total number of months. For a nominal annual rate compounded monthly, divide the rate by 12 and multiply years by 12.
With the same positive nominal annual rate, yes. Interest is credited sooner and begins earning interest, although the incremental gain shrinks as frequency rises.
The basic lump-sum formula does not. Use a future-value-of-annuity formula for equal periodic deposits or compound each irregular deposit for the time it is actually invested.
By the FinanceBrain Team · Last verified July 12, 2026 · How we produce and verify articles