Week 7 Annuity Payments that Occur at the Begining of Each Period

Week 7: Lecture

Annuity Payments That Occur At The Beginning Of Each Period

In “normal” annuities the periodic payments are assumed to occur at the end of each period. Occasionally, however, you encounter a situation in which the payments are made at the beginning of each period. Examples:

  • You want to invest a certain amount each month beginning today into an account to finance your child’s education.
  • You win the lottery and your winnings are to be paid to you at the beginning of each of the next 20 years.

When the payments are made makes a difference in the annuity’s PV or FV because you gain or lose a period of compounding. For example, what's the present value of a stream of 4 $100 payments to be paid to you at the beginning of the next four years: (r = 10%)

tvm_4pmt_annuity_timeline_beg_of_month.jpg

Solution:

tvm_pvifa_10per_3yrs.jpg

If you are solving for the FV of an annuity you make the adjustment for beginning of year payments a bit differently. For example, For example, what's the future value of a stream of 4 $100 payments to be paid to you at the beginning of the next four years: (r = 10%)

tvm_4pmt_annuity_timeline_end_of_month.jpg

Solution:

tvm_fvifa_10per_4years.jpg

 

Notice that it's the drawing of the timeline which keeps you organized in this problem. Always draw one if you can!