| TVM symbol | Meaning |
|---|---|
| N | total number of periods |
| I% | interest rate per year |
| PV | present value / initial amount |
| FV | future value / ending amount |
| P/Y and C/Y | payments per year and compounding periods per year |
Sign convention: If money leaves your pocket at the start, PV is usually entered as negative. If money comes back to you later, FV is positive. Opposite signs stop calculator errors.
Quick setup example
A saver invests $4 000 now. How would PV and FV usually be signed?
Step by step
- The saver pays money out now, so PV is negative.
- The future amount comes back later, so FV is positive.
Final answer
PV is usually negative and FV positive.
Worked setup example
Set up a TVM calculation for $5 000 invested at 4.8% per year for 6 years, compounded monthly.
Step by step
- Monthly compounding means 12 periods per year.
- Total periods:
- Interest rate stays annual in the TVM entry.
- Present value is money paid out now.
- No regular payments in this question.
- Use monthly settings.
Final answer
A correct TVM setup uses N = 72, I% = 4.8, PV = -5000, PMT = 0, P/Y = 12, C/Y = 12.
Common setup trap: Students often put N = 6 instead of 72 for monthly compounding. N must count periods, not years.
Know your predicted grade
Take timed mock exams and get detailed feedback on every answer. See exactly where you're losing marks.
The big idea: TVM is especially useful when the unknown is not the final value. IB often asks how long it takes, what starting amount is needed, or what rate is required.
Worked example — solve for time
A fund grows from 4 000 at 5% per year compounded yearly. What should you solve for, and how should the result be interpreted?
Step by step
- The unknown is the number of years, so solve for N.
- Enter PV and FV with opposite signs.
- If the calculator gives a non-integer value, the question may still need a whole-number interpretation.
Final answer
You solve for N, then interpret it according to the wording: exact years, nearest year, or first full year.
| Error | Why it happens | Fix |
|---|---|---|
| Wrong sign on PV/FV | Calculator expects cash-flow direction | Use opposite signs |
| Wrong N | Using years instead of periods | Convert years to total periods |
| Wrong P/Y or C/Y | Forgetting frequency settings | Match them to the question |
| Answer looks unrealistic | Setup mistake or wrong units | Check with rough mental estimate |
Sanity-check the answer: If 5% interest for a few years gives a final value smaller than the starting value, something has gone wrong. Quick common-sense checks catch many calculator-entry errors.