Question

38) A lottery ticket states that you will receive $250 every year for the next ten years. a. What is the present value of the winning lottery ticket if the discount rate is 6% and it is an ordinary annuity? b. What is the present value of the winning lottery ticket if the discount rate is 6% and it is an annuity due? c. What is the difference between the ordinary annuity and annuity due?

Answer 1

Answer:

Instructions are listed below.

Explanation:

Giving the following information:

A lottery ticket states that you will receive $250 every year for the next ten years.

A)  i=0.06      ordinary annuity

PV= FV/(1+i)^n

FV= {A*[(1+i)^n-1]}/i

A= annual payment

FV= {250*[(1.06^10)-1]}/0.06= $3,295.20

PV= 3,295.20/1.06^10=1,840.02

B) i=0.06 annuity due (beginning of the year)

FV= 3,295.20 + [(250*1.06^10)-1]= $3492.91

PV= 3492.91/1.06^10= $1,950.42

C) The interest gets compounded for one more period in an annuity due.