Finance Calculator

What is TVM?

The time value of money is the concept that money available today is worth more than the same amount in the future, due to its earning potential. A dollar today can be invested to grow into more than a dollar tomorrow.

The five TVM variables — N, I/Y, PV, PMT, and FV — are mathematically linked. If you know four, you can always solve for the fifth.

Present Value vs Future Value

Present Value (PV) is the current worth of a future sum or cash flow stream, discounted at the interest rate. A positive PV typically represents money received; a negative PV money paid out.

Future Value (FV) is how much a current investment will grow to at a given rate over N periods. Sign convention: inflows are positive, outflows negative. For a simpler future-value model with regular contributions, try the investment calculator.

Annuities & Payments

PMT represents a regular periodic payment — such as a mortgage payment, savings contribution, or coupon payment. Set PMT to 0 for lump-sum calculations (e.g., a savings bond with no interim payments).

An ordinary annuity makes payments at the end of each period; an annuity due (set timing to Beginning) pays at the start, resulting in slightly higher returns.

Compounding Frequency

P/Y sets how many payments occur per year; C/Y sets how often interest compounds. When they differ, an effective per-period rate is calculated automatically.

More frequent compounding produces slightly higher returns. A 6% annual rate compounded monthly has an effective annual rate (EAR) of about 6.168%, compounded daily ~6.183%. The compound interest calculator models growth at varying compounding frequencies.

Worked example

Solving for Future Value: PV = £10,000, I/Y = 5%, N = 10 years, PMT = 0 (lump-sum, no regular payments), P/Y = 1 → FV = £16,289. Alternatively, solving for PMT: to accumulate £20,000 in 5 years at 4% (monthly, P/Y = 12), set FV = 20,000, N = 60, I/Y = 4%, PV = 0 → PMT = £301/month.

What is the time value of money?

The time value of money (TVM) is the principle that money today is worth more than the same amount in the future, because money can be invested to grow. The five TVM variables — N, I/Y, PV, PMT, and FV — are mathematically linked; knowing any four lets you solve for the fifth.

What is the difference between present value and future value?

Present value (PV) is the current worth of a future sum, discounted at a given rate. Future value (FV) is how much a sum invested today will grow to after N periods. A positive value typically represents money received; a negative value money paid out — consistent sign convention is essential for correct results.

What is an annuity?

An annuity is a series of equal payments at regular intervals — such as monthly mortgage payments or savings contributions. PMT represents this periodic payment. Set PMT to zero for single lump-sum calculations. An ordinary annuity pays at the end of each period; an annuity due pays at the start.

How does compounding frequency affect my result?

More frequent compounding produces higher effective returns. A 6% annual rate compounded monthly has an EAR of about 6.168%; daily compounding gives about 6.183%. P/Y sets payments per year; C/Y sets compounding frequency. When they differ, the calculator automatically computes the effective per-period rate.