The five TVM keys
- N: the number of payments or periods (30 years of monthly payments is 360).
- I/Y: the interest rate per year, as a percent.
- PV: the present value, the amount at the start, like a loan you receive.
- PMT: the payment each period.
- FV: the future value, the amount at the end.
Signs: money in and money out
Like a BA II Plus or HP 12C, the signs show which way money moves. Money you receive is positive and money you pay out is negative. A $200,000 loan you receive (PV = 200,000) at 6% for 360 months is paid back with PMT = −$1,199.10. Saving $100 a month (PMT = −100) at 5% for 10 years grows to FV = $15,528.23.
The formula
PV × (1 + i)ᴺ + PMT × (1 + i·t) × ((1 + i)ᴺ − 1) ÷ i + FV = 0
Here i is the rate per payment period and t is 1 when payments are at the start of each period, 0 at the end. When P/Y and C/Y differ, i = (1 + I/Y ÷ C/Y)^(C/Y ÷ P/Y) − 1. Calcist solves for N with logarithms and for I/Y by narrowing in on the rate.