Time value of money

The time value of money is the greater benefit of receiving money now rather than an identical sum later. It is founded on time preference.Increasing percentage (g) F = D ⋅ n ( 1 + i ) n 1 + g {displaystyle F=Dcdot {frac {n(1+i)^{n}}{1+g}}}   (for i = g)Increasing percentage (g) P = D ⋅ n 1 + g {displaystyle P=Dcdot {frac {n}{1+g}}}   (for i = g) The time value of money is the greater benefit of receiving money now rather than an identical sum later. It is founded on time preference. 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. It also underlies investment. Investors are willing to forgo spending their money now only if they expect a favorable return on their investment in the future, such that the increased value to be available later is sufficiently high to offset the preference to have money now. The Talmud (~500 CE) recognizes the time value of money. In Tractate Makkos page 3a the Talmud discusses a case where witnesses falsely claimed that the term of a loan was 30 days when it was actually 10 years. 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.