Business Math: Ch13: Annuities and Sinking Funds

Jorgen Grace made deposits of $250 at the end of each year for 12 years. The rate received was 6% annually. What is the value of the investment after 12 years?

$ 4,217.485

Given the annuity due of $1,000 per year at 8% for 3 years, what is the future value at the end of Year 1? A) $1,000 B) $1,080 C) $2,080

$1,000 beginning of year investment × 1.08 = $1,080 balance at end of year.

At the beginning of each year for 14 years, Sherry Kardell invested $400 that earns 10% annually. What is the future value of Sherry's account in 14 years?

$12,708.99

Ted Williams made deposits of $500 at the end of each year for eight years. The rate is 8% compounded annually. The value of Ted's annuity at the end of eight years is (use the tables in the handbook):

$5,318.30

Given the annuity due of $10,000 per year at 10% for 2 years, match the value to the time frame. A) $10,000 B) $11,000 C) $21,000 D) $23,100

A) $10,000 > Beginning of Year 1 B) $11,000 > End of Year 1 C) $21,000 > Beginning of Year 2 D) $23,100 > End of Year 2

Judy invests $3,000 a year for 3 years into an ordinary annuity earning 7% per year. How much will Judy have at the end of Year 3? (Use the ordinary annuity table.) A) $9,644.70 B) $9,000 C) $22,987.50

A) $9,644.70 3,000 x 3.2149

Given an investment of $20,000 after 2 years made quarterly at 12%, match the table factor to the annuity type. A) 10.1591 B) 8.8923

A) 10.1591 > Annuity due B) 8.8923 > Ordinary annuity

Select all answers that identify an annuity: A) A series of payments that occur over regular payment periods. B) Payment term that includes payments from the beginning of the first payment period to the end of the last payment period. C) Future value = face value. D) Payments that are paid in a lump sum and are different that lottery payments.

A) A series of payments that occur over regular payment periods. B) Payment term that includes payments from the beginning of the first payment period to the end of the last payment period.

Regular deposits made at the beginning of the period (rent or insurance premiums).

Annuity Due

What is the term for a series of payments over a period of time.

Annunity

Given an annuity due of $2,000 per year at 8% per year for 4 years, what is the value of the investment at the end of Year 4? A) $9,012.20 B) $9,733.20 C) $11,733.20

B) $9,733.20

Perez wants to withdraw $10,000 at the end of each of 4 years. Interest is 6% annually. What is the correct table factor? A) 5.2421 B) 3.4651 C) 4.3746

B) 3.4651

Select the "true" statement about annuities due. A) You add one payment to the product of the table factor and the payment amount. B) It earns more interest than an ordinary annuity. C) It earns less interest than an ordinary annuity. D) You subtract one period when finding the table factor.

B) It earns more interest than an ordinary annuity.

The goal of a sinking fund is to determine the amount of the: A) present value of the investment B) periodic payment C) future value of the investment

B) periodic payment

Tracy wants to withdraw $1,000 at the end of each semiannual period for 3 years. Interest is 6% annually. How much must she invest today to receive this stream of payments? A) $2,673.0 B) $4,917.30 C) $5,417.20

C) $5,417.20

Greg invests $1,000 at the end of each year for 5 years at 5% annually, then leaves the investment to grow (without additional payments) for an additional 5 years. What is the future value of this investment after 10 years? A) $16,289 B) $12,577.90 C) $7,052.32

C) $7,052.32

Discharging bonded indebtedness, replacing worn-out equipment, or purchasing plant expansion are some of the uses of: A) simple interest B) present value C) sinking fund

C) sinking fund

(Contingent/Certain) annuities have a specific stated number of payments.

Certain

(Contingent/Certain) annunities have no fixed number of payments but depend on an uncertain event.

Contingent

A___________________ annuity depends on an uncertain event to occur, and has no fixed number of payments.

Contingent

Given the annuity due of $1,000 per year at 8% for 3 years, what is the future value at the end of Year 3? Calculate manually. A) $3,779.14 B) $3,240 C) $3,246.60 D) $3,506.11

D) $3,506.11

Scott deposits $5,000 at the end of each year into an account for five years. Assuming 6% interest annually, what is the value of his account in five years?

FV = Annual deposit x Future value interest factor of annuity = [(1 + r)N - 1] / r = [(1.06)5 - 1] / 0.06 = 0.3382 / 0.06 = 5.64 So, FV = $5,000 x 5.64 = $28,185.50

(True/False) Interest is not calculated in ordinary annuities.

False

True or false: An annuity is a lump-sum payment.

False

(True/False) An annuity is one lump sum payment.

False An annuity is a stream of payments

The future value of an annuity is the (present/future) dollar amount of a series of payments plus interest.

Future

What is the equation for a sinking fund.

Future Value x Sinking Fund Table Factor

An annuity due earns interest on one ___________ payment than an ordinary annuity.

More

Washington Investments needs $50,000 to replace their building's roof in 10 years time. They can earn an interest rate of 10% compounded annually. What amount will they need to invest at the end of each year to be able to cover the cost of the roof replacement in 10 years? A) $19,275 B) $5,000 C) $3,135

N = 10, i = 10%; table factor = .0627 × $50,000 = $3,135 per year.

Camille needs to replace her car in 2 years. How much per month does she need to put away to have $28,000 if she can earn 24% annual interest? A) $13,862.80 B) $1,166.67 C) $921.20

N = 12 months × 2 years = 24 periods. i = 24% ÷ 12 months = 2%; table factor = .0329 × $28,000 = $921.20.

Thomas wants to retire in 6 years. What amount should Thomas invest now to be able to withdraw $30,000 at the end of each year for 20 years after retirement if he can earn 8%? A) $294,543 B) $185,621

N = 20, i = 8%; PV of an annuity table factor = 9.8181 × $30,000 = $294,543. N = 6, i = 8%; PV of $1 at end of period = .6302 × $294,543 = $185,621.

Given an annuity due of $2,000 per year at 8% per year for 4 years, what is the value of the investment at the end of Year 4? A) $11,733.20 B) $9,733.20 C) $9,012.20

N = 4 + 1 = 5, i = 8%; table factor 5.8666 × $2,000 = $11,733.20 - $2,000 = $9,733.20.

Regular deposits made at the end of the period.

Ordinary Annuity

Carlyle plans to invest $12,000 per year for the next 5 years at 10% interest. How much will he have at the end of Year 1 for an ordinary annuity? A) $12,000 B) $13,200 C) $73,261.20 D) $15,200

The investment is made at the end of the period; therefore, it has not yet earned interest. At the end of Year 1 Carlyle's investment totals $12,000.

(True/False) An ordinary annuity results in the deposit or payment being made at end of the period.

True

(True/False) Maturity value is equal to principal plus interest.

True

(True/False) The value of an annuity is the series of payments and interest.

True

True or false: An annuity due payment does not have to be made annually.

True

True or false: Annuity payments can be made semiannually, monthly, or quarterly.

True

Annuity due payments are made:

at the beginning of each period, such as a rent payment.

In an ordinary annuity the interest on a yearly investment starts building interest:

at the end of the first period.

Bram Johnson invests $500 at the end of each quarter for 10 years. The account earns 12% interest annually. What is the value of the account at the end of 10 years? a. 37,700 b. 37,700.60 c. 37,000 d. 3,700

b. 37,700.60

A sinking fund accumulates interest using the (compound/simple) ___________ interest method.

compound

An annuity due earns (more/less)________________ interest than an ordinary annuity. The annuity due will give a higher final value.

more

The present value of an ordinary annuity looks at how much needs to be invested ______________ to receive a stream of payments for a given number of years in the ___________________.

now ; future