Question

7. Future value of annuities

There are two categories of cash flows: single cash flows, referred to as “lump sums,” and annuities. Based on your understanding of annuities, answer the following questions.

Which of the following statements about annuities are true? Check all that apply.

A perpetuity is a constant, infinite stream of equal cash flows that can be thought of as an infinite annuity.

An annuity due earns more interest than an ordinary annuity of equal time.

An annuity due is an annuity that makes a payment at the end of each period for a certain time period.

Ordinary annuities make fixed payments at the end of each period for a certain time period.

Which of the following is an example of an annuity?

A retirement fund set up to pay a series of regular payments

A fund that invests in technology companies and distributes quarterly dividends for two out of four quarters per year but not always the same quarters

Katie had a high monthly food bill before she decided to cook at home every day in order to reduce her expenses. She starts to save $1,410 every year and plans to renovate her kitchen. She deposits the money in her savings account at the end of each year and earns 5% annual interest. Katie’s savings are an example of an annuity. If Katie decides to renovate her kitchen, how much would she have in her savings account at the end of eight years?

$9,113.13

$11,444.60

$14,137.46

$13,464.24

If Katie deposits the money at the beginning of every year and everything else remains the same, she will save ________ by the end of eight years.

Answer 1

The true statements are:-

• A perpetuity is a constant, infinite stream of equal cash flows that can be thought of as an infinite annuity.

• An annuity due earns more interest than an ordinary annuity of equal time.

• Ordinary annuities make fixed payments at the end of each period for a certain time period.

The following is an example of the annuity:-

A retirement fund set up to pay a series of regular payments

FV if compounding at the end of year =FV(5%,8,-1410) =13464.24

FV if compounding at the beginning of year =FV(5%,8,-1410,,1) =14137.36