Question

7. Present value of annuities and annuity payments

The present value of an annuity is the sum of the discounted value of all future cash flows.

You have the opportunity to invest in several annuities. Which of the following 10-year annuities has the greatest present value (PV)? Assume that all annuities earn the same positive interest rate.

An annuity that pays $500 at the end of every six months

An annuity that pays $1,000 at the end of each year

An annuity that pays $500 at the beginning of every six months

An annuity that pays $1,000 at the beginning of each year

An ordinary annuity selling at $10,538.38 today promises to make equal payments at the end of each year for the next twelve years (N). If the annuity’s appropriate interest rate (I) remains at 6.50% during this time, the annual annuity payment (PMT) will be     .

You just won the lottery. Congratulations! The jackpot is $35,000,000, paid in twelve equal annual payments. The first payment on the lottery jackpot will be made today. In present value terms, you really won   —assuming annual interest rate of 6.50%.

8. Implied interest rate and period

Consider the case of the following annuities, and the need to compute either their expected rate of return or duration.

Matthew needed money for some unexpected expenses, so he borrowed $3,900.55 from a friend and agreed to repay the loan in four equal installments of $1,100 at the end of each year. The agreement is offering an implied interest rate of   .

Matthew’s friend, Gregory, has hired a financial planner for advice on retirement. Considering Gregory’s current expenses and expected future lifestyle changes, the financial planner has stated that once Gregory crosses a threshold of $4,136,860 in savings, he will have enough money for retirement. Gregory has nothing saved for his retirement yet, so he plans to start depositing $40,000 in a retirement fund at a fixed rate of 5.00% at the end of each year. It will take   for Gregory to reach his retirement goal.

9. Perpetuities

Perpetuities are also called annuities with an extended or unlimited life. Based on your understanding of perpetuities, answer the following questions.

Which of the following are characteristics of a perpetuity? Check all that apply.

A perpetuity is a stream of unequal cash flows.

The value of a perpetuity is equal to the sum of the present value of its expected future cash flows.

The value of a perpetuity cannot be determined.

A perpetuity is a stream of regularly timed, equal cash flows that continues forever.

A local bank’s advertising reads: “Give us $45,000 today, and we’ll pay you $800 every year forever.” If you plan to live forever, what annual interest rate will you earn on your deposit?

2.14%

1.60%

1.42%

1.78%

Oops! When you went in to make your deposit, the bank representative said the amount of required deposit reported in the advertisement was incorrect and should have read $67,500. This revision, which will   the interest rate earned on your deposited funds, will adjust your earned interest rate to   .

Answer 1

7)

Present value of future cash flows depends on the timing of occurrence of cash flows and interest rates. Payments received at year beginning will be more valuable than the payments received at year ending.

Hence, correct option is “An annuity that pays $1,000 at the beginning of each year”