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Bballry1234
April 27th 2009, 02:07 PM
Mary deposits 1000 into a fund at the beginning of each year for 10 years. At the end of 15 years, she makes an additional deposit of X.

At the end of 20 years, Mary uses the accumulated balance in the fund to buy a perpetuity immediate with annual payments of 2000 per year for 10 years, and 1000 per year thereafter.
interest in 5% effective.
Calculate X

Ok, can someone please tell me how they got the right side of the equation to be : 1000/.05 + 1000 A angle n

I get why the left side is 1000 s double dot 10 * 1.05 **10 +X*(1.5**5)

NoMoreExams
April 27th 2009, 02:18 PM
"perpetuity immediate with annual payments of 2000 per year for 10 years, and 1000 per year thereafter."

You can translate that into paying 1000 forever plus 1000 for the first 10 years right?

Bballry1234
April 27th 2009, 02:39 PM
yea, but I don't get why it's 1000 A angle n

Shouldn't it be 2000 A angle n?

NoMoreExams
April 27th 2009, 02:58 PM
yea, but I don't get why it's 1000 A angle n

Shouldn't it be 2000 A angle n?

Didn't you use up 1000 of that 2000 in your perpetuity already?

Once again:

"perpetuity immediate with annual payments of 2000 per year for 10 years, and 1000 per year thereafter."

Year 1 = 2000
Year 2 = 2000
:
Year 10 = 2000
Year 11 = 1000
Year 12 = 1000
:
forever

This is the same as
Year 1: 1000 + 1000
Year 2: 1000 + 1000
:
Year 10: 1000 + 1000
Year 11: 1000
year 12: 1000
:
forever

Or in other words 1000 forever and then 1000 for the first 10 years. So PV of 1000 forever is 1000/i and then add in the leftover 1000 for the first 10 years?

Bballry1234
April 27th 2009, 08:49 PM
OMG I get it now!!

Thank you so much..haha this problem was driving me crazy.

I seem to find the perpetuity problems the hardest

NoMoreExams
April 28th 2009, 01:36 PM
OMG I get it now!!

Thank you so much..haha this problem was driving me crazy.

I seem to find the perpetuity problems the hardest

You didn't have to do it that way, you could've said that's the same as

2000a_{10} + v^10 * 1000/i = 2000(1 - v^10)/i + 1000v^10/i = 2000/i - 2000v^10/i + 1000v^10/i = 1000/i + 1000/i - 1000v^10/i = 1000/i + 1000(1 - v^10)/i = 1000/i + 1000a_{10} as desired

PrinceKohli
May 1st 2009, 11:12 AM
Mary deposits 1000 into a fund at the beginning of each year for 10 years. At the end of 15 years, she makes an additional deposit of X.

At the end of 20 years, Mary uses the accumulated balance in the fund to buy a perpetuity immediate with annual payments of 2000 per year for 10 years, and 1000 per year thereafter.
interest in 5% effective.
Calculate X

Ok, can someone please tell me how they got the right side of the equation to be : 1000/.05 + 1000 A angle n

I get why the left side is 1000 s double dot 10 * 1.05 **10 +X*(1.5**5)

Can you please post the correct answer. I got 4865.1257

Thanks.

John 54
May 1st 2009, 11:02 PM
That's the correct answer.