Question

Future value of an annuity   

Using the values​ below, answer the questions that follow.  ​(Click on the icon located on the​ top-right corner of the data table below in order to copy its contents into a​ spreadsheet.)

Amount of annuity	Interest rate	Deposit period​ (years)
​$7,000	6​%	6

a.  Calculate the future value of the​ annuity, assuming that it is

​(1) An ordinary annuity.

​(2) An annuity due.

b.  Compare your findings in parts a​(1) and a​(2). All else being​ identical, which type of annuity—ordinary or annuity due—is preferable as an​ investment? Explain why.

a.​ (1) The future value of the ordinary annuity is $___. [Round to the nearest cent.)

***Thank you for your help!

Answer 1

Part A:

1)

FV of Annuity :

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here deposits are made at the end of the period. FV of annuity is future value of cash flows deposited at regular intervals grown at specified int rate or Growth rate to future date.

FV of Annuity = CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	$            7,000.00
Int Rate	6.000%
Periods	6

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 7000 * [ [ ( 1 + 0.06 ) ^ 6 ] - 1 ] / 0.06
= $ 7000 * [ [ ( 1.06 ) ^ 6 ] - 1 ] / 0.06
= $ 7000 * [ [1.4185] - 1 ] / 0.06
= $ 7000 * [0.4185] /0.06
= $ 48827.23
FV of ANnuity is $ 48827.23

2)

FV of Annuity Due:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here deposits are made at the begining of the period.FV of annuity is future value of cash flows deposited at regular intervals grown at specified int rate or Growth rate to future date.

FV of Annuity DUe = ( 1 + r ) * FV of Annuity

FV of Annuity = (1+r) * CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	$      7,000.00
Int Rate	6.000%
Periods	6

FV of Annuity Due = ( 1+ r) [ Cash Flow * [ [ ( 1 + r )^n ] - 1 ] /r ]
= ( 1 + 0.06 ) * [7000 * [ [(1+0.06)^6] - 1 ] / 0.06 ]
= ( 1.06 ) * [7000 * [ [( 1.06 ) ^ 6 ] - 1 ] / 0.06 ]
= ( 1.06 ) * [7000 * [ [ 1.4185 ] - 1 ] / 0.06 ]
= ( 1.06 ) * [ $ 48827.23 ]
= $ 51756.86

FV of Annuity Due = $ 51756.86

Part B:

FV of ANnuity is $ 48827.23

FV of Annuity Due = $ 51756.86

FV of Annuity Due = FV of Annuity ( 1 + Int Rate )

In Annuity due, all CFs are moved one Year ahead. Incase of ANnuity due we will have more amount. Hence Annuity due is suggested.