The Golden Rule
Cash flows must have opposite signs to work
+
Money IN
You receive it
ā
Money OUT
You pay it
Always ask: "Is this money coming TO me or going FROM me?" Your perspective determines the sign. Stay consistent throughout the entire problem.
Common Scenarios ā Click to See Details
Taking a Loan
Borrower's perspective
PV +
PMT ā
FV ā
Savings / Investment
Building wealth
PV ā
PMT ā
FV +
Buying a Bond
Investor's perspective
PV ā
PMT +
FV +
Issuing a Bond
Company's perspective
PV +
PMT ā
FV ā
Lottery / Annuity
Lump sum vs. payments
PV ā
PMT +
Stock Investment
Buy, hold, sell
PV ā
PMT +
FV +
Quick Reference Table
| Situation | PV | PMT | FV | Why? |
|---|---|---|---|---|
| Savings / Investment | ā | ā | + | Deposit now, withdraw later |
| Taking a Loan | + | ā | 0 | Receive now, pay back over time |
| Buying a Bond | ā | + | + | Pay price, receive coupons + face |
| Issuing a Bond | + | ā | ā | Receive price, pay coupons + face |
| Finding Loan Payment | + | CPT | 0 | Given loan amount, find payment |
| Finding Savings Deposit | 0 | CPT | + | Given goal, find required deposit |
| Finding Bond YTM | ā | + | + | Given price/coupons, find rate |
| NPV (Initial Investment) | CFā = ā | You spend money on the project | ||
| NPV (Operating Cash Flows) | CFāāā = + | Project generates money for you | ||
Common Mistakes to Avoid
Making Everything Positive
Students often enter all values as positive because "the problem doesn't have negatives." But the calculator needs opposite signs to work!
ā Fix: If PV and FV have the same sign, you'll get an error or nonsense.
Forgetting to Clear Previous Values
Old values from previous problems contaminate your answer. The calculator uses whatever is stored.
ā Fix: Always press [2ND] [CLR TVM] before starting a new problem.
Confusing Perspectives
A loan is +PV for the borrower but āPV for the lender. Same transaction, opposite signs!
ā Fix: Always ask "Whose perspective am I taking?" and stay consistent.
Getting Weird Answers
If your answer has an unexpected sign (like negative interest rate), your signs were wrong.
ā Fix: Draw a timeline first. Mark each cash flow as + or ā before touching the calculator.
š” Memory Trick
"Out of Pocket = Out of Positive"
When money leaves your pocket, it leaves positive territory.
When money enters your pocket, it enters positive territory.