Discounting

A$.$ A rate that represents the return on an investor's best available alternative investment of equal risk.

$\backslash$table$[[$Time value of money,V$,$B$.,\backslash$table$[[$A series of equal $($constant$)$ cash flows $($receipts or payments$)$ that are expected to$],[$continue forever.$]]],[$Amortized loan,$,$C$.,\backslash$table$[[$A concept that maintains that the owner of a cash flow will value it differently, depending$],[$on when it occurs.$]]],[$Ordinary annuity,grad,D$.,\backslash$table$[[$A value that represents the interest paid by borrowers or earned by lenders, expressed as$],[$a percentage of the amount borrowed or invested over a $12-$month period.$]]],[$Annual percentage rate,V$,$E$.,\backslash$table$[[$The process of determining the present value of a cash flow or series of cash flows to be$],[$received or paid in the future.$]]],[$Annuity due,grad,F$.,\backslash$table$[[$A cash flow stream that is created by an investment or loan that requires its cash flows to$],[$take place on the last day of each quarter and requires that it last for $10$ years.$]]],[$Perpetuity$,$grad,G$.,\backslash$table$[[$A series of equal cash flows that occur at the beginning of each of the equally spaced$],[$intervals $($such as daily, monthly, quarterly, and so on$).]]],[$Future value,$,$H$.,\backslash$table$[[$The name given to the amount to which a cash flow, or a series of cash flows, will grow$],[$over a given period of time when compounded at a given rate of interest.$]]],[$Amortization schedule,V$,$I.,$\backslash$table$[[$A type of security that is frequently used in mortgages and requires that the loan payment$],[$contain both interest and loan principal.$]]],[$Opportunity cost of funds,$,$J$.,\backslash$table$[[$A table that reports the results of the disaggregation of each payment on an amortized$],[$loan$,$ such as a mortgage, into its interest and loan repayment components.$]]]]$

Time value of money calculations can be solved using a mathematical equation, a financial calculator, or a spieadsheet. Which of the following equations can be used to solve for the present value of an annuity due?

$PM\frac{T}{r}$

PMT $\{\frac{(1+r{)}^n-1}{r}\}(1+r)$

PMT $x(\frac{1-[\frac{1}{(1+r{)}^1}]}{r})$

PMT $(\frac{1-[\frac{1}{(1+r{)}^1}]}{r})(1+r)$