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 Post subject: Present Value of an Annuity QuestionPosted: Sat, 3 Apr 2010 03:18:44 UTC
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Joined: Sat, 3 Apr 2010 03:12:17 UTC
Posts: 3
Hi,

I dont know how to calculate the Present Value of an annuity of $50 received at the end of each year for 10 years, with the first payment to be received at the end of the 6th year. Assuming a discount rate of 8% Could somebody explain to me how this works? what happens for the first 5 years? nothing is received? Any clarity would be much appreciated Thank you all Top  Post subject: Re: Present Value of an Annuity QuestionPosted: Sat, 3 Apr 2010 03:50:23 UTC  Moderator Joined: Mon, 29 Dec 2008 17:49:32 UTC Posts: 6066 Location: 127.0.0.1, ::1 (avatar courtesy of UDN) everettjsj2 wrote: Hi, I dont know how to calculate the Present Value of an annuity of$50 received at the end of each year for 10 years, with the first payment to be received at the end of the 6th year. Assuming a discount rate of 8%

Could somebody explain to me how this works? what happens for the first 5 years? nothing is received?

Any clarity would be much appreciated

Thank you all

Yes, no payment in the first 5 years. Payment at the end of 6th, 7th, ...., 15th year.

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 Post subject: Re: Present Value of an Annuity QuestionPosted: Sat, 3 Apr 2010 12:44:23 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 3724
Location: Ottawa Ontario
x = PV of $50 annuity, n = 10 PV now = PV of x, n = 5 _________________ Walked over to a beggar...he gave me a quarter... Top  Post subject: Posted: Mon, 5 Apr 2010 23:17:51 UTC  S.O.S. Newbie Joined: Sat, 3 Apr 2010 03:12:17 UTC Posts: 3 Thank you Denis, I dont quite follow. So this annuity of$50 received at the end of each year for 10 years, with the first payment to be received at the end of the 6th year.

First, we calculate the present value of the annuity over 10 years
discounted at 8%

PV(n=10) = $50*(1-[1.08]^-10)/0.08 =$355.50

But then, the first payment doesnt come in until the end of the 6th year. So what do we do next?

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 Post subject: Posted: Tue, 6 Apr 2010 04:21:55 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 3724
Location: Ottawa Ontario
Perhaps this'll make it clear:
Code:
0        228.34 *1
1        246.61
2        266.34
3        287.64
4        310.65
5        335.50 *2
6  -50   312.34
....
15 -50      .00

(*2) : this is the required amount at end of year#5 to permit annual
withdrawals of 50 from year#6 to year#15 : 10 years.
(your 355.50 is a typo, I guess?)

We next need the PV of this 335.50: 335.50 / 1.08^5 = 228.34 (*1).

S'that nuff?

Btw, you can combine the 2 calculations:
[\$50*(1 - 1.08^-10) / .08] / 1.08^5 = 228.34

_________________
Walked over to a beggar...he gave me a quarter...

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