what is the future value of an annuity 
the future value of an annuity is the value of a group of recurring payments at a certain date in the future assuming a particular rate of return or a discount rate the higher the discount rate the greater the annuity s future value as long as all of the variables surrounding the annuity are known such as payment amount projected rate and number of periods it is possible to calculate the future value of the annuity understanding the future value of an annuitybecause of the time value of money money received or paid out today is worth more than the same amount of money will be in the future that s because the money can be invested and allowed to grow over time by the same logic a lump sum of 5 000 today is worth more than a series of five 1 000 annuity payments spread out over five years formula and calculation of the future value of an annuitythe formula for the future value of an ordinary annuity is as follows an ordinary annuity pays interest at the end of a particular period rather than at the beginning as is the case with an annuity due p pmt 1 r n 1 r where p future value of an annuity stream pmt dollar amount of each annuity payment r interest rate also known as discount rate n number of periods in which payments will be made begin aligned text p text pmt times frac big 1 r n 1 big r textbf where text p text future value of an annuity stream text pmt text dollar amount of each annuity payment r text interest rate also known as discount rate n text number of periods in which payments will be made end aligned p pmt r 1 r n 1 where p future value of an annuity streampmt dollar amount of each annuity paymentr interest rate also known as discount rate n number of periods in which payments will be made ordinary annuities are more common but an annuity due will result in a higher future value all else being equal future value of an annuity duewith an annuity due payments are made at the beginning of each period so the formula is slightly different to find the future value of an annuity due simply multiply the formula above by 1 r p pmt 1 r n 1 r 1 r begin aligned text p text pmt times frac big 1 r n 1 big r times 1 r end aligned p pmt r 1 r n 1 1 r future value of an annuity examplelet s say someone decides to invest 125 000 per year for the next five years in an annuity that they expect to compound at 8 per year in this example the series of payments is a regular annuity in which the payments are made at the end of each period the expected future value of this payment stream using the above formula is as follows future value 125 000 1 0 08 5 1 0 08 733 325 begin aligned text future value 125 000 times frac big 1 0 08 5 1 big 0 08 733 325 end aligned future value 125 000 0 08 1 0 08 5 1 733 325 future value of an annuity duelet s use the same example as above but with an annuity due this means that each of the 125 000 payments was made at the beginning of each period its future value would be calculated as follows future value 125 000 1 0 08 5 1 0 08 1 0 08 791 991 begin aligned text future value 125 000 times frac big 1 0 08 5 1 big 0 08 times 1 0 08 791 991 end aligned future value 125 000 0 08 1 0 08 5 1 1 0 08 791 991 all else being equal the future value of an annuity due will be greater than the future value of an ordinary annuity because the money has had an extra period to accumulate compounded interest in this example the future value of the annuity due is 58 666 more than that of the ordinary annuity 