What is the time value of money?
A dollar you hold today is worth more than a dollar you will receive next year. Today's dollar can be invested, earn interest, or pay down debt immediately the promised dollar can't. That gap in usefulness is called the time value of money, and it is the single idea underneath almost every financial formula: loans, mortgages, retirement projections, and bond pricing all reduce to it.
Every time-value problem is built from five quantities. Fix any four and the fifth is determined:
- PV (present value) the amount of money at the start.
- FV (future value) the amount at the end, after interest has compounded.
- I/Y (interest per year) the annual rate at which money grows (or is discounted).
- N (number of periods) how long the money compounds.
- PMT (periodic payment) an optional recurring cash flow each period.
A quick example
Deposit $1,000 at 5% annual interest. After one year you have $1,050 the future value of $1,000 for one period at 5%. Leave it a second year and you earn interest on the original $1,000 and on the first year's $50, ending at $1,102.50. That extra $2.50 is compound interest: interest earned on interest. Over long horizons compounding dominates, which is why saving early matters more than most people expect.
Reading cash-flow signs
Like the classic BA II Plus and HP 12C calculators, this tool uses the cash-flow sign convention: money flowing toward you is positive, money flowing away is negative. A positive PV (a loan you received) with negative payments (repayment) yields an FV that is the remaining balance. When a result looks wrong, check the signs first.
Beginning vs. end of period
You can choose whether payments occur at the end of each period (an ordinary annuity typical for loans) or the beginning (an annuity due typical for rent). A beginning-of-period payment accrues one extra period of interest. The compounding setting works similarly: 6% compounded monthly is effectively about 6.17% per year.
Results are for education only and do not constitute financial advice.