Annuities

[i]. Suppose someone offered you the choice of two equally risky annuities, each paying $10,000 per year for five years. One is an ordinary (or deferred) annuity, the other is an annuity due. Which of the following statements is most correct?

a. 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.

b. The present value of the annuity due exceeds the present value of the ordinary annuity, while the future value of the annuity due is less than the future value of the ordinary annuity.

c. The present value of the annuity due exceeds the present value of the ordinary annuity, and the future value of the annuity due also exceeds the future value of the ordinary annuity.

d. 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.

e. Statements a and d are correct.

[ii]. A $10,000 loan is to be amortized over 5 years, with annual end-of-year payments. Given the following facts, which of these statements is most correct?

a. The annual payments would be larger if the interest rate were lower.

b. If the loan were amortized over 10 years rather than 5 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 5-year amortization plan.

c. The last payment would have a higher proportion of interest than the first payment.

d. The proportion of interest versus principal repayment would be the same for each of the 5 payments.

e. The proportion of each payment that represents interest as opposed to repayment of principal would be higher if the interest rate were higher.

[iii]. Which of the following is most correct?

a. The present value of a 5-year annuity due will exceed the present value of a...