Time Value of Money: the engine behind every financial decision
Why a rial today outweighs a rial next year, how the five TVM registers work, and the sign discipline that makes every calculator answer come out right.
Every financial decision — saving, borrowing, valuing a bond, comparing two projects — reduces to the same question: what is money tomorrow worth today? Time value of money (TVM) is the grammar of finance, and the five TVM registers are its alphabet. Master them once and a dozen worksheets on this site become obvious.
The core idea: compounding
Money can be invested to earn interest, so a sum held today is strictly more valuable than the same sum later. With a periodic rate i and N periods, the future value of a single sum is FV = PV × (1 + i)^N. In reverse, present value discounts a future amount back: PV = FV / (1 + i)^N. Compounding is what makes the curve bend upward — interest earns interest.
The five registers: N, I/Y, PV, PMT, FV
Any TVM problem fixes four of the five registers and solves the fifth. That is the entire workflow — on the BA II Plus and on FinScope alike.
| Register | Meaning | Typical unit |
|---|---|---|
| N | Number of compounding periods | months, years, quarters |
| I/Y | Interest rate per period | % (per period) |
| PV | Present value — a lump sum today | currency |
| PMT | Level payment each period (annuity) | currency |
| FV | Future value — a lump sum at the end | currency |
Sign convention: money out is negative
The single most common source of wrong answers is ignoring signs. The calculator thinks in cash flows from your pocket: money you pay out is negative, money you receive is positive. Invest 100 today and you hand it over, so PV = −100; receive 161.051 at the end, so FV = +161.051. A loan looks the same from the borrower's side with the signs flipped.
Worked example: 100 grows to 161.051
- Clear the TVM registers (2ND CLR TVM on the BA II Plus, or «Clear all» in FinScope).
- N = 5 — five annual compounding periods.
- I/Y = 10 — ten percent per period.
- PV = −100 — you pay 100 today.
- PMT = 0 — no level payments.
- CPT FV → 161.051 — the engine-verified result.
The same registers can be solved backwards. How long does money take to double at 10%? Set PV = −1000, FV = 2000, I/Y = 10, PMT = 0 and solve for N: the answer is 7.2725 years — a precise version of the famous rule of 72.
Ordinary annuity vs annuity due (BGN)
When a level payment PMT runs for N periods, timing matters. In an ordinary annuity payments fall at the end of each period (END mode); in an annuity due they fall at the start (BGN mode). Each payment in a due annuity compounds one extra period, so results scale by exactly (1 + i). Save 100 per year for 5 years at 10%: the ordinary annuity reaches a future value of 610.51, while the annuity due reaches 671.561 — and 671.561 = 610.51 × 1.10. Present values follow the same law: 379.0787 ordinary versus 416.9865 due.
P/Y: payments per year
Real loans pay monthly, bonds pay semi-annually. The P/Y setting tells the calculator how many payments occur per year: with P/Y = 12, N counts months and the periodic rate is the annual quoted rate divided by twelve. FinScope exposes P/Y directly in the TVM worksheet and shows I/Y both per period and annualized, so you always know which rate the engine is using.
Frequently asked questions
Why must PV be negative?
Because the calculator tracks cash flows from your own pocket. Investing 100 today means 100 leaves you, so PV = −100, while the amount you later receive (FV = +161.051) is positive. If both inputs carry the same sign, the equation has no meaningful solution and the calculator either errors out or returns a nonsense rate.
What exactly does BGN mode change?
BGN (begin mode) treats each annuity payment as occurring at the start of the period instead of the end. Every payment then compounds for one additional period, so every PV and FV of the payment stream scales by exactly (1 + i): the 5-year, 100/year, 10% annuity jumps from FV 610.51 to 671.561 and from PV 379.0787 to 416.9865.
How does the P/Y setting work?
P/Y (payments per year) defines the period length. With P/Y = 12, N counts months and the interest rate used per period is the annual quoted rate divided by 12. On the BA II Plus you enter the annual rate in I/Y and the calculator divides internally; FinScope's TVM worksheet keeps the same discipline and shows the solved I/Y both per period and annualized, so the two never get confused.
Practice it live
Open the matching worksheet and reproduce every number in this article.
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