Finance Calculator: Universal TVM Solver
Professional-grade TVM calculator to solve for Present Value, Future Value, Interest Rate, Payment, or Periods. How to calculate PV and FV. Master the Time Value of Money. No sign-upโall calculations run locally.
The 5 TVM Variables Explained
Variable Definitions
- N (Periods):Total number of compounding periods. For monthly payments over 10 years, N = 120.
- I/Y (Interest Rate):Annual interest rate as a percentage. The calculator converts to periodic rate automatically.
- PV (Present Value):Today's value. For loans, PV is positive (you receive money). For investments, PV is negative (you deposit money).
- PMT (Payment):Regular periodic payment. Loan payments are negative (outflow); annuity receipts are positive (inflow).
- FV (Future Value):Value at end of time horizon. Investment growth is positive; loan balloon payment is negative.
Understanding each variable is essential for accurate calculations:
The core TVM relationship for a lump sum:
For periodic payments (annuity), PMT links PV, FV, r, and n through the standard annuity formulas. The calculator solves iteratively when a variable is unknown.
Common Use Cases
Investment Growth (Solve for FV)
- Inputs:N = periods, I/Y = expected return, PV = initial investment (negative), PMT = regular contributions (negative)
- Example:$10,000 initial + $500/month for 20 years at 7% = $299,145
- Tip:Check inflation-adjusted value for realistic retirement planning
How much will my investment be worth?
Loan Payment (Solve for PMT)
- Inputs:N = loan term in months, I/Y = annual rate, PV = loan amount (positive), FV = 0
- Example:$300,000 mortgage at 6.5% for 30 years = $1,896/month
- Tip:Result is negative (outflow) because you're paying
What will my monthly payment be?
Rate Discovery (Solve for I/Y)
- Inputs:N = periods, PV = amount borrowed, PMT = payment made, FV = remaining balance
- Use Case:Verify car dealer financing, compare loan offers, calculate investment returns
- Tip:Uses Newton-Raphson iteration for precision
What interest rate am I really paying?
Advanced Concepts
Annuity Types
- Ordinary Annuity (End):Payments at period end. Most loans, mortgages, and bonds.
- Annuity Due (Begin):Payments at period start. Rent, leases, insurance premiums.
- Impact:Annuity due earns one extra period of interestโabout 3% more over 30 years at 7%
Payment timing significantly affects calculations:
Compounding Frequency
- Monthly (12/year):Most loans, credit cards, savings accounts
- Quarterly (4/year):Some bonds, CDs, dividend stocks
- Annually (1/year):Simple loans, some international bonds
- Effect:More frequent compounding = slightly higher effective rate
How often interest is calculated and added:
Finance Calculator FAQ
? How do I use the TVM solver?
Select which variable you want to calculate (N, I/Y, PV, PMT, or FV) using the buttons at the top. Enter values for the other four variables. The calculator will solve for the missing piece. Remember: use negative values for money leaving your pocket (outflows) and positive for money coming to you (inflows).
? Why is my result showing as a negative number?
Negative numbers represent cash outflows (money you pay). Positive numbers represent cash inflows (money you receive). If solving for PMT on a loan, a negative result means you're making payments. If solving for FV on an investment, a positive result means you'll receive that amount. This "sign convention" is standard in professional finance.
? What is the difference between an ordinary annuity and an annuity due?
An ordinary annuity (End) has payments at the end of each periodโlike most mortgages and loans. An annuity due (Begin) has payments at the beginningโlike rent or lease payments. Annuity due payments earn one extra period of interest, yielding about 3% more over 30 years at typical rates.
? How do I calculate the interest rate on a loan?
Select "I/Y" as the variable to solve. Enter N (number of payments), PV (loan amount, positive because you receive it), PMT (payment amount, negative because you pay it), and FV (usually 0 for a fully amortized loan). The calculator uses Newton-Raphson iteration to find the precise annual rate.
? What does N represent in a finance calculator?
N is the total number of compounding periodsโnot necessarily years. If compounding monthly for 10 years, N = 120. If quarterly for 5 years, N = 20. The calculator adjusts the interest rate (I/Y) based on your selected compounding frequency to calculate the correct periodic rate.
? Why should I consider inflation when calculating Future Value?
A dollar today buys more than a dollar in 20 years due to inflation. Our calculator shows "inflation-adjusted" FV to reveal purchasing power. At 3% inflation, $1M in 20 years equals about $550K in today's dollars. For retirement planning, the real (inflation-adjusted) number matters more than the nominal figure.