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

55%

88

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

55%

88

Explanation / Answer

(a)(1) Ordinary annuity means at the cash flow at the end of the period

The Present value is calculated using =PV() function in excel as in =PV(rate,nper,pmt,fv,type) where rate = 5.5% = 0.055, nper = 88 years, pmt =14,000 , PV=0 and type =0 (ordinary annuity)

The present value of ordinary annuity =PV(0.055,88,14000,0,0) = 252,256.97

(2) If it's annuity due, we make the type =1 in the above function

Present value of an annuity due =PV(0.055,88,14000,0,1) = 266,131.10

(b) Annuity due has a higher present value than ordinary annuity since theannuity is received at the beginning of the year rather than at the end of the year.

All else being identical Annutiy Due has a higher present value

Reason: Annuity is received at the beginning of ther period rather than at the end.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.