Present value of an annuity Consider the following case.(Click on the icon locat

Question

Present value of an annuityConsider the following case.(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

Period (years)

$14 comma 00014,000

5%

8

a.Calculate the present 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

annuitylong dash—ordinary

or annuity

duelong dash—yields

a higher present value? Explain why.

The present value of the ordinary annuity is

$nothing.

(Round to the nearest cent.)

Amount of annuity

Interest rate

Period (years)

$14 comma 00014,000

5%

8

Explanation / Answer

PV of annuity = PMT*(1-(1+r)-n) / r

PV = 14000*(1-(1+5%)-8) / 5% = 90484.98

Pv of annuity due = PMT + PMT*(1-(1+r)-(n-1)) / r

                             = 14000 + 14000*(1-(1+5%)-8) / 5% = 95009.23

PV of annuity due is higher because it does payments in the beginning of the period (stars payments immeditely), whereas ordinary annuity does at the end of the period.

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