Future Value (Nominal)
$0.00
Future Value Calculator
Use this future value calculator to project how much your money can grow with compound interest. It supports a starting lump sum, regular contributions, flexible compounding and contribution frequency, beginning/end timing, annual fees, and inflation adjustment—ideal for investors, planners, and students who want precise, transparent projections.
Calculator
Affects how values are formatted.
$
$
%
How often interest is credited to the balance.
You can use decimals (e.g., 10.5 years).
Beginning = annuity due; End = ordinary annuity.
Results
Inflation-Adjusted Future Value
$0.00
Total Contributions (Principal)
$0.00
Total Interest Earned
$0.00
Effective Annual Rate (after fees)
0.00%
Assumptions
—
Data Source and Methodology
Authoritative Data Source: OpenStax, “Algebra and Trigonometry, 2nd ed., Section on Compound Interest,” 2022. Direct link: https://openstax.org/details/books/algebra-and-trigonometry-2e. Supplementary reference: U.S. Securities and Exchange Commission (SEC), “Compound Interest Calculator,” investor.gov.
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
The Formula Explained
Let i be the nominal annual rate, m the compounding periods per year, p the contribution periods per year, and t the number of years.
Periodic compounding rate: r_m = i / m, number of compounding periods: N = m t.
Equivalent contribution-period rate: r_c = (1 + r_m)^{m/p} - 1, number of contribution periods: M = p t.
Present value growth:
FV_{PV} = PV \cdot (1 + r_m)^{N}
Future value of an ordinary annuity (end-of-period contributions):
FV_{PMT,\;ord} = PMT \cdot \frac{(1 + r_c)^{M} - 1}{r_c}
Future value of an annuity due (beginning-of-period contributions):
FV_{PMT,\;due} = PMT \cdot \frac{(1 + r_c)^{M} - 1}{r_c} \cdot (1 + r_c)
Total nominal future value:
FV = FV_{PV} + FV_{PMT}
Inflation-adjusted (real) future value, with inflation rate \pi:
FV_{\text{real}} = \frac{FV}{(1 + \pi)^{t}}
Effective annual rate (after fees f): with net nominal rate i_{net} = i - f,
EAR = \left(1 + \frac{i_{net}}{m}\right)^{m} - 1
Periodic compounding rate: r_m = i / m, number of compounding periods: N = m t.
Equivalent contribution-period rate: r_c = (1 + r_m)^{m/p} - 1, number of contribution periods: M = p t.
Present value growth:
FV_{PV} = PV \cdot (1 + r_m)^{N}
Future value of an ordinary annuity (end-of-period contributions):
FV_{PMT,\;ord} = PMT \cdot \frac{(1 + r_c)^{M} - 1}{r_c}
Future value of an annuity due (beginning-of-period contributions):
FV_{PMT,\;due} = PMT \cdot \frac{(1 + r_c)^{M} - 1}{r_c} \cdot (1 + r_c)
Total nominal future value:
FV = FV_{PV} + FV_{PMT}
Inflation-adjusted (real) future value, with inflation rate \pi:
FV_{\text{real}} = \frac{FV}{(1 + \pi)^{t}}
Effective annual rate (after fees f): with net nominal rate i_{net} = i - f,
EAR = \left(1 + \frac{i_{net}}{m}\right)^{m} - 1
Glossary of Variables
PV: Initial investment (present value) you invest today.
PMT: Regular contribution added each contribution period.
i: Nominal annual interest rate (APR), in decimal (e.g., 0.07 for 7%).
f: Annual fees (expense ratio, advisory fees), in decimal.
m: Compounding periods per year (1, 2, 4, 12, 365, etc.).
p: Contribution periods per year (1, 4, 12, etc.).
t: Time in years.
r_m: Rate per compounding period (i_net / m).
r_c: Rate per contribution period (converted from compounding): (1 + r_m)^(m/p) - 1.
FV: Nominal future value at the end of t years.
FV_real: Inflation-adjusted future value in today's money.
EAR: Effective annual rate after fees.
How It Works: A Step-by-Step Example
Suppose you invest PV = $5,000, add PMT = $200 at the end of each month, earn i = 7% APR with monthly compounding (m = 12), for t = 10 years. Fees f = 0%, inflation π = 2%.
- Compute periodic rates: r_m = i/m = 0.07/12 ≈ 0.0058333; since p = m = 12, r_c = r_m. N = 120, M = 120.
- Grow the lump sum: FV_PV = 5,000 × (1 + 0.0058333)^120 ≈ $10,167.57.
- Grow the monthly contributions: FV_PMT = 200 × [(1 + 0.0058333)^120 − 1] / 0.0058333 ≈ $34,409.39.
- Total nominal FV: FV ≈ $44,576.96. Total contributions = 5,000 + 200 × 120 = $29,000. Interest earned ≈ $15,576.96.
- Real FV: FV_real = FV / (1 + 0.02)^10 ≈ $36,606.67.
Frequently Asked Questions (FAQ)
Is the annual interest rate nominal or effective?
It is nominal (APR). The compounding frequency converts this APR into periodic growth. The EAR output shows the equivalent effective annual rate after fees.
How are different contribution and compounding frequencies handled?
The calculator converts the compounding-period rate into an equivalent contribution-period rate using r_c = (1 + r_m)^(m/p) − 1, then applies the standard annuity formula.
What if my fee is higher than the APR?
That yields a negative net rate (i − f). The tool supports this and will project declining value accordingly, as long as the rate is greater than −100% per year.
Can I model a one-time investment only?
Yes. Set PMT to 0 and enter your initial amount in PV. The tool will compute the compounded value of your lump sum.
Does the inflation adjustment change contributions?
No. Inflation is applied at the end to the total future value to express it in today’s purchasing power.
Which currency should I choose?
Choose the currency you prefer for display. It doesn’t change the math—only formatting and symbols.