HP 12C sign convention for CFA TVM problems

The HP 12C uses a cash-flow story for Time Value of Money (TVM). Money the candidate parts with is negative. Money the candidate receives is positive. If both Present Value (PV) and Future Value (FV) are on the same side of the cash flow with no Payment (PMT), the calculator has no real rate to solve and surfaces an error.

This page explains the convention, the CHS key, and how to fix the common Error 0 case. Charterly's free HP 12C calculator catches this state under rule H5 and explains the convention in the warning instead of returning a cryptic error code.

The cash-flow story

A TVM problem describes movement of money over time, from the candidate's perspective:

• Money the candidate parts with is negative. Deposits, loan disbursements (from the lender's view), bond purchases.
• Money the candidate receives is positive. Withdrawals, loan repayments (from the lender's view), bond coupons and redemption.

The HP 12C requires this convention because TVM is solving for a rate that connects two-sided cash flows. Same-sign PV and FV with no PMT is not solvable: the engine has no positive return rate that turns money you have into more money you have without something going the other way.

The CHS key

CHS (Change Sign) flips the sign of the value currently in the X register. To store -1,000 in PV:

1. Type 1000. X = 1,000.
2. Press CHS. X = -1,000.
3. Press PV. PV register now holds -1,000.

CHS is its own key, not a shifted function. Many CFA candidates expect a +/- toggle and miss CHS on first inspection.

A worked example

Problem. A candidate deposits 1,000 today, contributes 200 at the end of each year for 5 years, and earns 6 percent annually. Compute the FV.

Cash-flow story: the candidate parts with 1,000 today, parts with 200 every year, and receives the FV at the end.

Keystrokes:

1. f FIN (clear financial registers)
2. 5 then n
3. 6 then i
4. 1000 then CHS then PV (cash out)
5. 200 then CHS then PMT (cash out)
6. FV

Expected FV: 2,465.6442.

The FV register holds a positive number because the candidate receives the accumulated balance at the end. PV and PMT are negative because they are cash out.

The Error 0 case (same-sign PV and FV)

Problem. Same candidate, but the candidate stores both PV and FV as positive numbers because the sign convention is forgotten.

Keystrokes:

1. f FIN
2. 5 then n
3. 6 then i
4. 1000 then PV (positive; should have been -1,000)
5. 200 then CHS then PMT
6. FV

The HP 12C does not raise a hard error here because PMT is non-zero and the engine can still solve. The returned FV is a number that does not match any answer choice, and the candidate is left guessing whether the formula was wrong.

A harder case. Same problem but with PMT = 0 and PV and FV both positive. Now the HP 12C returns Error 0. There is no rate that solves the implied cash-flow story.

Fix. Decide which leg is the candidate's money out and which is the candidate's money in, press CHS on whichever you stored on the wrong side, and re-solve.

How Charterly catches this

Rule H5 fires when PV and FV are both stored with the same sign and PMT is zero. The Charterly warning surfaces before the engine returns Error 0: "HP TVM expects opposite signs for PV vs FV when PMT is zero. Flip the sign on one of them." The result is still computed; the engine returns a clean error code rather than crashing, and the warning explains the cause in plain language.

The BA II Plus parallel rule is M4. The keystroke fix on the TI side is +/- instead of CHS. See the BA II Plus CFA guide for the TI version.

Related pages

• HP 12C stack mistakes for the RPN stack hygiene that lives next to sign convention on every problem.
• NPV and IRR on the HP 12C for the same convention applied to cash-flow registers.
• The twelve CFA calculator mistakes for the named-rule list.

Frequently asked questions

Why does the HP 12C not return a clear "wrong sign" error? Because there is no general rule that says one sign is right and the other is wrong; it depends on the candidate's cash-flow story. The engine surfaces Error 0 when no real rate connects the inputs and a regular wrong-looking answer when the inputs technically solve but do not match the intended problem.

Does the sign convention apply to the bond keys (`f PRICE`, `f YTM`)? Yes. The bond functions reuse the TVM registers under the hood. PV, PMT, and FV carry the same convention.

Can I just always type CHS on PV and not worry? For most CFA problems, yes. PV is the candidate's outlay (cash out, negative) in over 90 percent of exam questions. The exceptions are problems framed from a counterparty's view (a bond issuer, a lender) or problems where PV is solved-for rather than typed.

Does Charterly auto-flip the sign? No. Charterly surfaces a warning and explains the convention. It never silently changes inputs (AGENTS section 7).

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