Question

(a) What is the future value of a 4-year ordinary (regular) annuity of $2,750 if the appropriate interest rate is 5.6%? (b) What is the present value of this 4-year ordinary annuity? (c) What would the i) future, and ii) present value, be if this annuity were an annuity due (still 4 years)? Hint: set your calculator to BGN, there is a video in M2 that shows you how to do this. Don’t forget to reset to “END” after you work an annuity due problem. FV = PV =

Compare the results you got in part b for present and future value of a "regular" annuity and compare these to the values you got for the annuity due (part c). What is the relationship that you see? Using the time value of money concepts you have learned so far, why does this relationship (PV of regular annuity vs. annuity due and FV of regular annuity vs. annuity due occur? Pleas show work.

Answer 1

a)
Future value of regular annuity is calculated by using the following excel formula:
=FV(rate,nper,pmt,pv)
=FV(5.6%,4,-2750,0)
= $11,958.98

Future value of regular annuity = $11,958.98

b)
Present value of regular annuity is calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(5.6%,4,-2750,0)
= $9,616.97

Present value of regular annuity = $9,616.97

c)
Future value of annuity due is calculated by using the following excel formula:
=FV(rate,nper,pmt,pv,beginning of the period)
=FV(5.6%,4,-2750,0,1)
= $12,628.68

Future value of annuity due = $12,628.68

Present value of annuity due is calculated by using the following excel formula:
=PV(rate,nper,pmt,fv,beginning of the period)
=PV(5.6%,4,-2750,0,1)
= $10,155.52

Present value of annuity due = $10,155.52

The Present value of regular annuity is less than the Present value of annuity due. The future value of regular annuity is less than the future value of annuity due. The present and future value of annuity due is greater than the regular annuity.