BA II Plus: the TVM keys as one equation of value
N, I/Y, PV, PMT and FV are five slots in a single present-value equation. Fill four, solve for the fifth.
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One equation, five variables
The five TVM keys hold the terms of PV + PMT·aₙ + FV·vⁿ = 0 with the sign convention applied. Every level-annuity, loan or accumulation question is that equation with one unknown, which is why the same four keystrokes answer questions that look unrelated.
A level annuity present value
Twelve annual payments of 2,500 at 6% effective, first payment in one year.
| Keys | Effect |
|---|---|
| 12 · N | Twelve periods. |
| 6 · I/Y | Six percent per period — entered as 6, not 0.06. |
| 2500 · PMT | The level payment. |
| 0 · FV | No balloon payment. Always set this explicitly. |
| CPT · PV | Returns −20,959.61: the value today of payments you receive. |
Switching to an annuity-due
2ND · BGN · 2ND · SET · 2ND · QUIT puts the calculator in begin mode, which shifts every payment one period earlier. The BGN indicator stays on screen until you switch it back, and forgetting to is one of the most common self-inflicted errors on Exam FM. Switch it on, use it, switch it off in the same breath.
Solving for the rate
Entering N, PV, PMT and FV and pressing CPT · I/Y solves for the interest rate by iteration — this is how you get a bond yield or a loan's implied rate without bisecting by hand. The result is a rate per PERIOD, so a semiannual bond gives a semiannual yield that must be doubled for a nominal annual quote or squared up for an effective annual one.