Question

What is the present value of a 20-year $10,000 ordinary annuity paid annually and earning 6% interest? In other words, if an ordinary annuity paid $10,000 annually for 20 years, earning 6% interest, what is the present value this annuity?

Answer 1

PV of Annuity:  
   
Annuity is series of cash flows that are deposited at regular intervals for specific period of time.  
  
PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r  
r - Int rate per period = 6 % or 0.06
n - No. of periods = 20

Particulars	Amount
Cash Flow	$          10,000.00
Int Rate	6.0000%
Periods	20

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 10000 * [ 1 - [(1+0.06)^-20]] /0.06
= $ 10000 * [ 1 - [(1.06)^-20]] /0.06
= $ 10000 * [ 1 - [0.3118]] /0.06
= $ 10000 * [0.6882]] /0.06
= $ 114699.21

Present value of annuity =  $ 114699.21