Time Value of Money Calculator
Solve for any variable in time value of money equations: present value, future value, payment, periods, or interest rate.
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Time Value of Money Concepts
The current worth of a future sum of money, discounted at a specific rate. Used to determine how much to invest today to reach a future goal.
The value of a current asset at a specified date in the future, assuming growth at a certain rate. Shows how investments grow over time.
The regular payment made into or out of an investment or loan. Can be calculated for annuities, loan payments, or savings contributions.
The rate at which money grows or the cost of borrowing. This rate is critical to all TVM calculations and determines growth/cost over time.
Frequently Asked Questions
The Five TVM Variables: PV, FV, PMT, N, and I/Y
Every time value of money problem involves five variables: Present Value (PV), Future Value (FV), Payment (PMT), Number of Periods (N), and Interest Rate per Year (I/Y). Given any four of these, you can solve for the fifth. Financial calculators (HP 12C, TI BA II Plus) and spreadsheet functions are built around this 5-variable framework.
| Variable | Symbol | Common Uses | Example |
|---|---|---|---|
| Present Value | PV | Loan principal, initial investment, current price | $250,000 mortgage |
| Future Value | FV | Balloon payment, target savings, maturity value | $1,000,000 retirement goal |
| Payment | PMT | Monthly loan payment, periodic savings deposit | $1,500/month mortgage payment |
| Number of Periods | N | Months in a loan, years to retirement | 360 months (30-year mortgage) |
| Interest Rate | I/Y | Loan APR, investment return, discount rate | 6.5% annual mortgage rate |
Sign convention is critical: cash outflows (money you pay) are negative, and cash inflows (money you receive) are positive. For a loan: PV is positive (you receive the loan proceeds), PMT is negative (you make payments), and FV is typically 0 (loan fully repaid). For savings: PV is negative (you invest money), PMT is negative (you add deposits), and FV is positive (you receive the accumulated balance).
Annuity vs Lump Sum: Ordinary Annuity and Annuity Due
An ordinary annuity has payments at the end of each period — mortgages, car loans, and most investment contributions follow this pattern. An annuity due has payments at the beginning — rent, insurance premiums, and lease payments are examples. The annuity due always has a slightly higher present/future value because each payment has one additional period to compound.
For a $1,000 monthly payment at 6% annual rate over 10 years (120 periods): the future value of an ordinary annuity is $163,879. The future value of an annuity due is $164,699 — a difference of $820. Over longer periods and higher rates, this gap widens. At 8% over 30 years, the difference between ordinary and due for a $500/month payment is approximately $5,200.
A perpetuity is a special annuity with an infinite number of payments. Its present value simplifies to PV = PMT / r. A perpetuity paying $5,000/year discounted at 5% has a present value of $100,000. A growing perpetuity (where payments grow at rate g) uses: PV = PMT / (r - g). A $5,000 annual payment growing at 2% with a 5% discount rate is worth $166,667. This formula underpins the Gordon Growth Model used for stock valuation.
TVM in Loan Amortization and Mortgage Calculations
Loan amortization is a direct application of TVM. A $300,000 30-year fixed mortgage at 6.5% produces a monthly payment of $1,896 using the PMT formula. In the first month, $1,625 (85.7%) goes to interest and only $271 (14.3%) to principal. By month 180 (halfway through), the split shifts to approximately $1,088 interest and $808 principal. In the final year, nearly all of the $1,896 payment goes to principal.
| Mortgage Amount | Rate | Term | Monthly Payment | Total Interest Paid |
|---|---|---|---|---|
| $300,000 | 6.5% | 30 years | $1,896 | $382,633 |
| $300,000 | 6.5% | 15 years | $2,613 | $170,388 |
| $300,000 | 5.0% | 30 years | $1,610 | $279,767 |
| $500,000 | 7.0% | 30 years | $3,327 | $697,544 |
Choosing a 15-year term over 30-year increases the monthly payment by $717 but saves $212,245 in total interest — a dramatic demonstration of how the number of periods (N) impacts total cost. Making just one extra payment per year on a 30-year mortgage (13 payments instead of 12) typically shaves 4-5 years off the loan and saves $50,000-$80,000 in interest on a $300,000 mortgage at 6.5%.