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

Question

Which of the following statements about annuities are true? Check all that apply. When equal payments are made at the end of each period for a certain time period, they are treated as an annuity due. A perpetuity is a series of equal payments made at fixed intervals that continue infinitely and can be thought of as an infinite annuity. When equal payments are made at the end of each period for a certain time period, they are treated as ordinary annuities. An ordinary annuity of equal time earns less interest than an annuity due. Which of the following is an example of an annuity? O 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 O An investment in a certificate of deposit (CD) 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 $1,270 in her bank account, which pays her 5% interest annually. Ashley wants to keep saving for two 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 two years? O $2,733.68 O $2,212.98 $2,361.45 o $2,603.50 If Ashley deposits the money at the beginning of every year and everything else remains the same, she will save by the end of two years

Explanation / Answer

1) the following statements are true about annuity:

a) A perpetuity is a series of equal payments made at fixed intervals that continue infinitely and can be thought of as an infinite annuity

b) when equal payments are made at the end of each period for a certain time period, they are treated as ordinary annuities

c) An ordinary annuity or equal time earns less interest than an annuity due

this is because payments are made sooner in an annuity due

2) An annuity is a series of equal payments made for a defined period of time. Example of annuity is ,

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

3)

amount deposited annually , A = $1270

period of investment , n = 2 years

rate of interest , r = 5 % = 0.05

at the end of 2 years , amount of money Ashley will have, X = [1270*(1+r)2 ] + [ 1270*(1+r)]

= [1270*(1.05)2 ] + [ 1270*(1.05)] = 1400.175 + 1333.5 = $2733.675 or $2733.68 ( rounding off to 2 decimal places)

4) if Ashley deposity money at the beginning of every year and everything else remains the same , she will save an amount = X*(1+r) = 2733.675*(1.05) = $2870.358 or $2870.36 ( rounding off to 2 decimal places)

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