AtlasCalcsUtility Calculation Suite
2026-09-23 6 min read

Time Value of Money Calculator

Lump sum plus stream in one equation.

Calculator

Present Value
$
Payment Per Period
$
Interest Rate (per period)(%)
%
Number of Periods

Results

Optimal

Future Value

$102,723.18

Total Contributions

$60,000.00

Interest Earned

$42,723.18

Live results update as you type — currently showing future value of $102,723.18. Replace the defaults with your own numbers.

Visualizations

TVM Build

60,000$Contributions
42,723$Interest

Formula

Lump sum plus annuity in one equation.

FV = PV(1+r)^n + PMT((1+r)^n−1)/r

Variables

SymbolNameUnitDescription
PVLump$
PMTPayment$

Explanation

Combined growth of lump + stream.

Step-by-Step Calculation

Follow each step to understand how the result is calculated from your inputs.

Step 1

FV = PV×(1+r)^n + PMT×((1+r)^n−1)/r

Result: $102,723.18
Final Answer
$102,723.18

Worked Examples

See how the calculator works with different scenarios.

Scenario

The time value of money calculator run on the values above.

Inputs

presentValue:50000
payment:1000
rate:6
periods:10

Calculation

1. FV = PV×(1+r)^n + PMT×((1+r)^n−1)/r → $102,723.18

Result

Future Value: $102,723.18

Interpretation

$102,723.18 from $50,000.00 plus $1,000.00 × 10 at 6.00%.

Understanding Your Result

Your Result: Future Value: $102,723.18

What This Means

Combined growth of lump + stream.

Why It Matters

$102,723.18 from $50,000.00 plus $1,000.00 × 10 at 6.00%.

Professional Interpretation

$102,723.18 from $50,000.00 plus $1,000.00 × 10 at 6.00%.

How this is calculated

Lump sum plus annuity in one equation.

What drives the result

Compounding grows lump sums and streams forward; discounting shrinks them back. The rate is the exchange rate between today and tomorrow.

Recommendations

  • •Solve any leg: PV, PMT, rate or periods.
  • •Ordinary (end) timing assumed — due adds (1+r).

Educational Content

Introduction

Money has a time price: a dollar today compounds forward and discounts backward. Annuities package that into streams, NPV/IRR judge projects, and DCF prices whole firms.

Concept Explanation

Compounding grows lump sums and streams forward; discounting shrinks them back. The rate is the exchange rate between today and tomorrow.

Applications

▸Saving and loan decisions
▸Project screening with NPV/IRR
▸Firm valuation with DCF

Benefits

  • •Comparable across timing
  • •Rate-explicit decisions
  • •Value linked to cash, not accounting

Limitations

  • •Constant-rate simplifications
  • •Even-flow shortcuts where noted
  • •Forecasts dominate DCF truth

Best Practices

  • •Match rate frequency to cash frequency
  • •Show ranges for DCF/IRR
  • •Annualize before comparing

Common Misconceptions

Myth: Nominal equals effective
Truth: Compounding gaps them — use EAR.
Myth: IRR alone decides
Truth: Scale and timing need NPV beside it.

Practical Tips

  • •Draw the timeline first.

Common Mistakes

Sign errors
Inflows vs outflows.

Assumptions

This calculator makes the following assumptions to provide estimates:

Ordinary timing: Standard.

Limitations

Be aware of these limitations when using this calculator:

Limitation: Constant-rate simplifications
Limitation: Even-flow shortcuts where noted
Limitation: Forecasts dominate DCF truth

Frequently Asked Questions

Answers to common questions about this calculator.

Solve any leg?
PV, PMT, r or n.
How accurate is the time value of money calculator?
It follows the stated TVM formula from your inputs. Match rate frequency to cash frequency for exact results.
Ordinary vs due?
Ordinary pays at period-end; due pays at start and is worth (1+r) more.
Nominal vs effective?
Nominal ignores compounding; effective (EAR) includes it — compare EAR.

Related Guides

Deepen your understanding with these educational resources.

Glossary

Technical terms used in mortgage calculations explained in plain language.

Present value
What a future sum is worth today after discounting.
Future value
What a present sum grows to with compounding.
Annuity
Equal payments each period for a fixed term.

Authoritative References

Trusted sources and standards referenced by this calculator.

Applicable Standards

End-of-period (ordinary) timing unless labeled dueMoney rounded for display only; math at full precisionEven annual flows where labeled; uneven timing needs period detail

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Page Information

Last Updated:

2026-09-23

Version:

2.0.0

License:

Free to use for educational and professional purposes.