| TVM symbol | Meaning |
|---|---|
| N | total number of periods |
| I% | interest rate per year |
| PV | present value / initial amount |
| PMT | payment per period (0 if no regular payments) |
| 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.
Why P/Y = 12 and C/Y = 12?: Monthly compounding means interest is added 12 times each year.
- P/Y = 12 → each period is one month. That is why N = 72 for 6 years, not 6.
- C/Y = 12 → the calculator divides 4.8% by 12 and uses 0.4% per month automatically.
- In IB problems P/Y and C/Y almost always match: both 12 for monthly, both 4 for quarterly, both 1 for yearly.
Common setup trap: Students often put N = 6 instead of 72 for monthly compounding. N must count periods, not years.
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Regular deposits — when PMT ≠ 0:
- PV = lump sum put in at the start.
- PMT = fixed amount added every period.
- Sign rule: PV and PMT must have the same sign — both negative if money leaves your pocket.
IB-style question: A student deposits 100.
- (a) Find the balance after 2 years, correct to 2 decimal places. [3 marks]
- (b) Find the number of complete months for the balance to first exceed $5 000. [2 marks]
Part (a) — find the balance after 2 years
What is FV after 24 months?
Step by step
- N = 24 (2 years × 12 months).
- I% = 4. The GDC divides by 12 per month automatically.
- Both the opening deposit and the top-ups leave the pocket — negative.
- P/Y = 12, C/Y = 12. Cursor on FV → solve.
Final answer
FV = $3 577.43
Part (b) — solve for N
After how many complete months does the balance first exceed $5 000?
Step by step
- Same setup as part (a). Now N is unknown and FV is known.
- The target comes back to the student → positive.
- PV = −1000, PMT = −100 unchanged — money still going out.
- Cursor on N → solve.
- 36 months is not enough. Round UP — the question says 'first exceeds'.
Final answer
37 complete months
Two things students get wrong:
- PMT sign: if PV is negative, PMT must also be negative. Both represent money leaving your pocket.
- Rounding N: the GDC gives 36.5, not 37. Always round up for 'first exceeds' or 'how many complete months'.
| 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.