Question

# Suppose someone offered you the choice of two equally risky annuities, each paying \$10,000 per year...

Suppose someone offered you the choice of two equally risky annuities, each paying \$10,000 per year for five years. One is an ordinary annuity, the other is an annuity due. Which of the following statements is most correct (assume a positive discount rate)?

the present value of the annuity due exceeds the present value of the ordinary annuity, but the future value of an annuity due may is less than the future value of the ordinary annuity

the present value of the annuity due exceeds the present value of the ordinary annuity, and the future value of an annuity due is greater than the future value of the ordinary annuity

none of the other answers are correct

if interest rates increase, the difference between the present value of the ordinary annuity and the present value of the annuity due remains the same

the present value of the ordinary annuity must exceed the present value of the annuity due, but the future value of an ordinary annuity may be less than the future value of the annuity due

The correct statement is

the present value of the annuity due exceeds the present value of the ordinary annuity, and the future value of an annuity due is greater than the future value of the ordinary annuity

Payment are made/received at the end of the period under ordinary annuity while they are made/received at the begininng of the year under annuity due

Hence, the present value as well as future value of annuity due is more (due to one year additional interest)