For an income or payment stream with a different payment schedule, the interest rate must be converted into the relevant periodic interest rate.For example, a monthly rate for a mortgage with monthly payments requires that the interest rate be divided by 12 (see the example below).If you are using a financial calculator or a spreadsheet, you can usually set it for either calculation.The following formulas are for an ordinary annuity.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.The solutions may be found using (in most cases) the formulas, a financial calculator or a spreadsheet.
For example, the future value sum There are several basic equations that represent the equalities listed above.An important note is that the interest rate i is the interest rate for the relevant period.For an annuity that makes one payment per year, i will be the annual interest rate.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.(In the case of a debt, cash flows are payments against principal and interest; in the case of a financial asset, these are contributions to or withdrawals from the balance.) More generally, the cash flows may not be periodic but may be specified individually.