Consider three investment alternatives: a perpetuity, an ordinary annuity, and an annuity due. All three have the same payment amount. The annuity due and the ordinary annuity have the same number of payments and the number of payments is greater than one. The interest rate is positive and the same for all three investments.
Given this information which of the following statements is correct?
a. The present value of the perpetuity is less than the present value of the ordinary annuity.
b. The perpetuity and the ordinary annuity have the same present value.
c. The ordinary annuity and the annuity due have the same present value.
d. The present value of the ordinary annuity is less than the present value of the perpetuity.
e. The present value of the annuity due is less than the present value of the ordinary annuity.
Explain to me why each answer is wrong or correct