Annuities and Sinking Funds

A sinking fund is a different type of (blank)

annuity

Assuming all other factors are the same (payment, rate of return, etc.), why will an investor have a greater future value with an annuity due than from an ordinary annuity?

Because a payment is made at the beginning of the year, interest starts sooner.

True or False: An annuity due requires that payments be made at the beginning of the period.

True

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

True

The present value of an ordinary annuity looks at how much needs to be invested (blank 1) to receive a stream of payments for a given number of years in the (blank 2)

blank 1- today blank 2- future

a lottery deposits a sum of money in a bank; the growth of this sum of money through (blank) is what allows the lottery winner to receive a series of payments

blank- compound interest

To free up money for large and expensive future expenses, many people find it necessary to (blank) present spending habits

cut expenses

An annuity due earns (blank) interest than an ordinary annuity.

more

Determining the amount of the annual (blank) is the second step in using the FV of an annuity formula

payment

Within the formula for calculating future value of an ordinary annuity, the first step is to calculate the number of (blank) and the rate for each one.

periods

Discharging bonded indebtedness, replacing worn-out equipment, or purchasing plant expansion are some of the uses of:

sinking fund

$5000 will be set aside annually for five years (compounded as an ordinary annuity) at 5% per year. What is the future value (rounded to nearest penny).

$27,628.16

Using a financial calculator to compute the FV of an ordinary annuity, which ingredient is entered as a negative number (cash outflow)?

Annual payment amount

Match the annuity type to the respective definition.

Annuities Certain- Have a fixed number of payments. (such as a home loan) Contingent Annuities- Have no fixed number of payments. (such as death of the policy holder)

Match the annuity group with the timing of payments?

Annuity Due- Payments are made at the beginning of the period. Ordinary Annuity- Payments are made at the end of the period.

Thomas wants to retire in 6 years. What amount should Tom 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%

Answer: $185,612.95 Formula: $30,000((1-1/(1.08)^20)/.08= $294,544.42; $294,544.42/ (1.08)^6= $185,612.95

Washington Investments needs $50,000 to replace their building's roof in 10 years. 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.

Answer: $3,137.27 Formula: N=10, i= 10% ($50,000 x.10)/ (((1+10)^10)-1)=$3,137.27

Tracy wants to withdraw $1,000 at the end of each semiannual period for 3 years. Interest is 6% annually.

Answer: $5,417.19 Formula: N= 3 years x semiannual= 6, i=6% annual / semiannual= 3%; 1,000((1-1/ (1.03)^6)/ .03= $5,417.19

$3000 will be set aside annually for three years (compounded as an ordinary annuity) at 8% per year. What is the future value?

$9,739.20

When planning for retirement, investors need to know what kinds of information for effective decision making?

- What do I need to do now so that I will have the money I need in the future (payments)? - How much money will I need in the future (lump sum)?

Order the steps for manually calculating future value of an annuity due.

1. Calculate the interest on the period's balance and add it to the balance. 2. Add additional investment at the beginning of the period to the new balance. 3. Continue calculating interest and adding it and the additional investment until the desired period is reached.

The maturity value of an ordinary annuity can be calculated by which of these methods?

1. Manually, with year-to-year calculations 2. Using the FV formula 3. Using a financial calculator

Order the steps for manually calculating future value of an ordinary annuity.

1. No interest is calculated on the first period. 2. Calculate interest on the balance, and add the interest to the previous balance. 3. Add additional investment at the end of the second period to the new balance. 4. Continue calculating interest on balance, adding to previous balance, then adding additional investment until desired period is reached.

Given the ordinary annuity formula, A=Pmt x [(1+i)^n-1/i match the term to the definition

A- Future value or an ordinary annuity i- Interest n- Number of periods Pmt- Annuity payment

When calculating interest and future value of an ordinary annuity, money is invested at what point in the year (period)?

At the end of each period

Increasing the number of compounding periods (such as moving from annual compounding to quarterly compounding), what will be the net effect on the FV of both an ordinary annuity and an annuity due?

Both will increase in FV

Match the future values of a lump-sum and an annuity

Lump-sum- Principal plus interest. Annuity- Future dollar amount of a series of payments plus interest.

When using a calculator to determine PV of an ordinary annuity, which variable is entered as a negative number?

PMT

When solving for PV of an annuity, the formula is based on given information which includes the interest rate, compounding periods, and what?

Payment expected from the annuity