Question

Present value of an annuity   

Consider the following case.  

Amount of annuity	Interest rate	Period​ (years)
​$44,000	12​%	13

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 annuity—ordinary or annuity due—is ​preferable? Explain why.

The present value of the ordinary annuity is____.  (Round to the nearest​ cent.)

Answer 1

- Perioidic amount of annuity = $44,000

1). Calculating the present value of ordinary annuity:-

Where, C= Periodic Payments = $44,000

r = Periodic Interest rate = 12%

n= no of periods = 13

Present Value of ordinary annuity = $282,636.13

2). Calculating the present value of annuity due:-

Where, C= Periodic Payments = $44,000

r = Periodic Interest rate = 12%

n= no of periods = 13

Present Value of annuity Due= $316,552.47

- In Ordinary annuity, amount received or payments made are incurred at the end of period while in annuity due it is at the beginning of the perid.

Since in annuity due cashflows inccurrs at the beginning of the period which decreases its discounting period and increases it Present Value. Thus, Annuity due is Preferable.

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