how an annuity table works
an annuity table provides a factor based on time and a discount rate interest rate by which an annuity payment can be multiplied to determine its present value for example an annuity table could be used to calculate the present value of an annuity that paid 10 000 a year for 15 years if the interest rate is expected to be 3 according to the concept of the time value of money receiving a lump sum payment in the present is worth more than receiving the same sum in the future having 10 000 today is better than being given 1 000 per year for the next 10 years because the sum could be invested and earn interest over that decade at the end of the 10 year period the 10 000 lump sum would be worth more than the sum of the annual payments even if invested at the same interest rate annuity table and the present value of an annuitythe formula for the present value of an ordinary annuity as opposed to an annuity due is as follows p pmt 1 1 r n r where p present value of an annuity stream pmt dollar amount of each annuity payment r interest rate also known as the discount rate n number of periods in which payments will be made begin aligned text p text pmt times frac 1 1 r n r textbf where text p text present value of an annuity stream text pmt text dollar amount of each annuity payment r text interest rate also known as the discount rate n text number of periods in which payments will be made end aligned p pmt r1 1 r n where p present value of an annuity streampmt dollar amount of each annuity paymentr interest rate also known as the discount rate n number of periods in which payments will be made assume an individual has an opportunity to receive an annuity that pays 50 000 per year for the next 25 years with a discount rate of 6 or a lump sum payment of 650 000 he needs to determine the more rational option using the above formula the present value of this annuity is pva 50 000 1 1 0 06 25 0 06 639 168 where pva present value of annuity begin aligned text pva 50 000 times frac 1 1 0 06 25 0 06 639 168 textbf where text pva text present value of annuity end aligned pva 50 000 0 061 1 0 06 25 639 168where pva present value of annuity given this information the annuity is worth 10 832 less on a time adjusted basis and the individual should choose the lump sum payment over the annuity note this formula is for an ordinary annuity where payments are made at the end of the period in the above example each 50 000 payment would occur at the end of the year each year for 25 years with an annuity due the payments are made at the beginning of the period in question to find the value of an annuity due multiply the above formula by a factor of 1 r p pmt 1 1 r n r 1 r begin aligned text p text pmt times left frac 1 1 r n r right times 1 r end aligned p pmt r1 1 r n 1 r if the above example were of an annuity due its value would be p 50 000 1 1 0 06 25 0 06 1 0 06 677 518 begin aligned text p 50 000 quad times left frac 1 1 0 06 25 0 06 right times 1 0 06 677 518 end aligned p 50 000 0 061 1 0 06 25 1 0 06 677 518 in this case the individual should choose the annuity due because it is worth 27 518 more than the lump sum payment rather than working through the formulas above you could alternatively use an annuity table an annuity table simplifies the math by automatically giving you a factor for the second half of the formula above for example the present value of an ordinary annuity table would give you one number referred to as a factor that is pre calculated for the 1 1 r n r portion of the formula the factor is determined by the interest rate r in the formula and the number of periods in which payments will be made n in the formula in an annuity table the number of periods is commonly depicted down the left column the interest rate is commonly depicted across the top row simply select the correct interest rate and number of periods to find your factor in the intersecting cell that factor is then multiplied by the dollar amount of the annuity payment to arrive at the present value of the ordinary annuity below is an example of the present value of an ordinary annuity table if we take the example above with a 6 interest rate and a 25 year period you will find the factor 12 7834 if you multiply this 12 7834 factor from the annuity table by the 50 000 payment amount you will get 639 170 almost the same as the 639 168 result in the formula highlighted in the previous section the slight difference in the figures reflects the fact that the 12 7834 number in the annuity table is rounded there is a separate table for the present value of an annuity due and it will give you the correct factor based on the second formula 