The five TVM values
- N: number of periods.
- I/Y: interest rate per period.
- PV: present value, the amount at the start.
- PMT: the payment each period.
- FV: future value, the amount at the end.
These five are linked by one equation, so knowing any four determines the fifth. Mortgages, savings plans, annuities and bonds are all special cases.
The sign convention
Like the Texas Instruments BA II Plus and HP 12C, this solver uses cash-flow signs: money leaving your pocket is negative and money coming in is positive. To find what an investment grows to, enter the deposit and payments as negatives; the future value comes out positive. If you get an error that the values can't balance, check the signs.
Example
Investing $20,000 today (PV = −20,000) plus $2,000 at the end of each year (PMT = −2,000) for 10 years at 6% grows to FV = $62,178.54.
Frequently asked questions
Is I/Y per year or per period?
Per period. For monthly periods, divide the annual rate by 12 and multiply years by 12 for N.
What does “payments at the start” mean?
It's an annuity due, such as rent or insurance paid in advance. Each payment earns one extra period of interest.