See compound interest for details on converting between different periodic interest rates.The rate of return in the calculations can be either the variable solved for, or a predefined variable that measures a discount rate, interest, inflation, rate of return, cost of equity, cost of debt or any number of other analogous concepts.

This principle allows for the valuation of a likely stream of income in the future, in such a way that annual incomes are discounted and then added together, thus providing a lump-sum "present value" of the entire income stream; all of the standard calculations for time value of money derive from the most basic algebraic expression for the present value of a future sum, "discounted" to the present by an amount equal to the time value of money.

For example, the future value sum There are several basic equations that represent the equalities listed above.

The false witnesses must pay the difference of the value of the loan "in a situation where he would be required to give the money back (within) thirty days..., and that same sum in a situation where he would be required to give the money back (within) 10 years...

The difference is the sum that the testimony of the (false) witnesses sought to have the borrower lose; therefore, it is the sum that they must pay." The notion was later described by Martín de Azpilcueta (1491–1586) of the School of Salamanca.

If you want the answer for the present value of an annuity due simply multiply the PV of an ordinary annuity by (1 i).

The following formula use these common variables: The present value formula is the core formula for the time value of money; each of the other formulae is derived from this formula.

Time value of money problems involve the net value of cash flows at different points in time.

In a typical case, the variables might be: a balance (the real or nominal value of a debt or a financial asset in terms of monetary units), a periodic rate of interest, the number of periods, and a series of cash flows.

The time value of money is the greater benefit of receiving money now rather than later. The principle of the time value of money explains why interest is paid or earned: Interest, whether it is on a bank deposit or debt, compensates the depositor or lender for the time value of money. Investors are willing to forgo spending their money now if they expect a favorable return on their investment in the future.

Historically in Christian societies, and in many Islamic societies today, charging any interest at all would be considered usury.

If you are using a financial calculator or a spreadsheet, you can usually set it for either calculation.

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