Question

6. 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.

Annuities are structured to provide fixed payments for a fixed period of time.

When equal payments are made at the beginning of each period for a certain time period, they are treated as an annuity due.

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

When equal payments are made at the beginning of each period for a certain time period, they are treated as ordinary annuities.

Which of the following is an example of an annuity?

A lump-sum payment made to a life insurance company that promises to make a series of equal payments later for some period of time

An investment in a certificate of deposit (CD)

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 $1,060 every year and plans to renovate her kitchen. She deposits the money in her savings account at the end of each year and earns 14% 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 seven years?

$11,374.32

$4,545.60

$12,966.73

$9,668.17

If Katie deposits the money at the beginning of every year and everything else remains the same, she will save $12,966.73 / $16,208.41 / $11,374.32 / $5,181.99 by the end of seven years.

Answer 1

The following are the true statements about the annuities

-Annuities are structured to provide fixed payment for a fixed period of time

-When equal payments are made at the beginning of each period for a certain period, they are treated as an annuity due

-An ordinary annuity of equal time earns less interest than an annuity due

The following is an example of an annuity

A lump-sum payment made to a life insurance company that promises to make a series of equal payments later for some period of time

The amount she will have in her savings account at the end of seven years

Annual Payment (P) = $1,060

Annual Interest Rate (r) = 14.00% per year

Number of years (n) = 7 Years

Therefore, Future Value of an Ordinary Annuity = P x [{(1+ r)ⁿ - 1} / r ]

= $1,060 x [{(1 + 0.14)⁷ - 1} / 0.14]

= $1,060 x [(2.502268791 – 1) / 0.14]

= $1,060 x [1.502268791 / 0.14]

= $1,060 x 10.73049137

= $11,374.32

Amount at the end of seven years if the deposits are made at the beginning of each year

The Future Value of an Annuity Due = Future Value of an Ordinary Annuity x (1 + Interest rate)

= $11,374.32 x (1 + 0.14)

= $11,374.32 x 1.14

= $12,966.73

If Katie deposits the money at the beginning of every year and everything else remains the same, she will save $12,966.73 by the end of seven years.