Calculate Future Value
Compound interest calculator for calculating the future value of an investment with fixed interest rates
FV Calculator
FV Calculation
Calculates the future value of your investment with compound interest based on regular payments or initial capital.
Example & Explanation
Example: FV Calculation
FV Formula
Basic Formula:
\[FV = PV \times (1 + r)^n + PMT \times \frac{(1 + r)^n - 1}{r}\]
Components:
- PV = Present Value (initial investment)
- PMT = Regular payment per period
- r = Interest rate per period
- n = Number of periods
Result: Future value with compound interest
What is FV (Future Value)?
- FV = Future Value = Value at future point in time
- Calculates value of investment after a fixed time
- Accounts for compound interest on all payments
- Helps with financial planning & wealth building
- Foundation for evaluating investment returns
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Mathematical Foundations of Future Value (FV)
The FV (Future Value) calculation combines compound interest with regular payments:
FV with Initial Value (PV)
Compound interest on initial investment
FV with Regular Payments
Compound interest on annuity payments
Description of Arguments
Interest Rate
The interest rate is the return per period (e.g., 6% per year). Select whether the interest rate is specified monthly or annually. The calculator automatically accounts for compound interest effects.
Duration (Years and Months)
The duration is the time period over which the investment runs. Specify years and additional months (e.g., 2 years and 6 months). Longer duration increases the compound interest effect.
Initial Value (PV - Present Value)
The initial value is the one-time capital investment at the beginning. This can be a savings deposit or loan origination, for example. Set this to 0 if you only have regular payments.
Regular Payment (PMT)
Regular payments are constant payments per period (e.g., $200 per month). Select the payment frequency (monthly, quarterly, semi-annually, or annually). Negative values represent withdrawals.
Due Date
The due date determines when payments occur: End of period (ordinary, payment at end of period) or Beginning of period (annuity due, payment at beginning).
Results
The results show two values: Future Value (FV) is the total capital after the duration, and Interest Earned is the earned interest.
Quick Reference
Standard Example
Payment Frequency
• Monthly: 12 per year
• Quarterly: 4 per year
• Semi-annually: 2 per year
• Annually: 1 per year
Use Cases
• Savings plan calculation
• Annuity calculation
• Loan comparison
• Wealth building
• Investment analysis
Future Value - Detailed Explanation
Fundamentals
The FV (Future Value) is a central function of financial calculations that computes the value of an investment after a certain time.
The future value of an investment consists of the principal and accumulated interest (compound interest).
Compound Interest Effect
The compound interest effect is key to building wealth:
Compound Interest Components
1. Principal: Money invested
2. Interest: Return on principal
3. Compound Interest: Return on returns
4. Time Effect: Longer duration = exponential growth
Practical Applications
FV is used in many financial questions:
• How much money will I have after 10 years?
• What will my savings plan grow to?
• How does my investment grow?
Key Factors
These factors influence the future value:
Influencing Factors
- Interest Rate (higher = faster growth)
- Time Period (longer = more compound interest)
- Payment Frequency (more often = more capital)
- Initial Amount (more = exponential growth)
Practical Calculation Examples
Example 1: Savings Plan
Scenario: Regular savings plan
Deposit: $500/Month
Interest Rate: 4% per year
Duration: 5 years
Future Value: = $33,149
Example 2: Lump Sum Investment
Scenario: One-time investment
Capital: $10,000
Interest Rate: 5% per year
Duration: 10 years
Future Value: = $16,470.09
Example 3: Combined
Scenario: Initial capital + savings
Start: $5,000
Monthly: $250 additional
Interest Rate: 4.5% per year
Future Value after 7 years: = $31,477.41
Calculation Tips
- Units: Stay consistent (years or months)
- Interest Rate: Enter with correct frequency
- Payments: Negative for withdrawals
- Due Date: Consider beginning vs. end timing
- Comparison: Run different scenarios
- Decimal Places: More for accuracy
Key Insights
The Power of Compound Interest
Small regular payments over time can grow into substantial wealth. Example: $100 monthly over 30 years at 5% interest yields over $60,000.
Start Early
Starting early with savings maximizes compound interest benefits. A 10-year head start can double your final value!
Interest Rate Sensitivity
The difference between 3% and 5% interest over 20 years is enormous. 1-2% more interest can result in 30-50% more future value.
Inflation Impact
Consider inflation: A nominal FV of $100,000 in 10 years is worth less than today. Real return = Nominal return - Inflation rate.