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ID: 2821877 • Letter: D
Question
Due to a bug in Google Chrome, this page may not function correctly. Click here to learn more. 6. Future value of annuities There are two categories of cash fiows: 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 K Ordinary annuties make fixed payments at the end of each period for a certain time period A perpetuity is a constant, infinite stream of equal cash flows that can be thought of as an infinite annuity. X An annuity due earns more interest than an ordinary annuity of equal time. X An annuity due is an annuity that makes a payment at the end of each period for a certain time period. Which of the following is an example of an annuity? O 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 A retirement fund set up to pay a series of regular payments Ashley has a large and growing collection of animated movies. She wants to replace her old television with a new LCD model, so she has started saving for it. At the end of each year, she deposits $1,060 in her bank account, which pays her 12% interest annually. Ashley wants to keep saving for six years and then buy the newest LCD model that is available. Ashley's savings are an example of an annuity. How much money will Ashley have to buy a new LCD TV at the end of six years? o $4,358.09 o $8,602.10 $9,634.35 O $7,311.79 If Ashley deposits the money at the beginning of every year and everything else remains the same, she will save by the end of six years.Explanation / Answer
1) Which are true statements
Only statement 4 is false.All others are true. statement 4 is false because in annuity due we are making payments at the begining of each period. Since annuity due makes payment sooner it has higher present value than an ordinary annuity,hence higher interest rate than an ordinary annuity. In an ordinary annuity equal payments are made at the end of each period for certain period. If it is for infinite time it forms a perpetuity.
2) Example for annuity
You have correctly selected the option.A retirement fund set up to pay a series of regular payments.
3) Future Value of Annuity
Future value of Annuity = A [((1+r)n-1) / r]
Where
A - Annuity payment = 1060
r - rate per period = 12%
n - no. of periods = 6
Future value of Annuity =1060* [((1+.12)6-1) / .12]
= 1060 * 8.1151890432
= 8,602.10 (Option B)
If deposited money at the begining of the period-
Future value of Annuity Due = Future value of Annuity * (1+r)
= 8602.10 * 1.12
= 9,634.35
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