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 Financial Mathematics Old FM Forum

#1
11-05-2018, 03:21 AM
 Sullinator Member SOA Join Date: Aug 2018 College: West Chester Universiy Posts: 119
FM question

Mr. Prescott donated 40,000 toward a future scholarship. The scholarships are to be paid according to the following schedule:

End of year1: 1,000
End of year2: 1500
End of year3: 2000

And so on...

with the amount of increasing 500 each year until scholarship reaches 5,000. The annual scholarship will remain at 5,000 until the fund is depleted. If the account balance is less than 5,000 at the end of any year (i.e. after awarding of the 5,000 for that year), that remaining amount immediately will be awarded as a smaller scholarship, and the account will be closed. The scholarship fund earns interest earns interest at an effective annual rate of 8%. Determine how many full 5,000 scholarships will be awarded.

How come in the solution everything was moved up to time 8 to solve for n?
#2
11-05-2018, 08:22 AM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,039

Quote:
That quote is from a different thread, but same idea. Include your thoughts, and give people enough info. In FM, there are frequently multiple valid approaches, all ok, all giving the same answer. You didn´t even tell us what they did, and you expect us to tell us why they did what they did?

As discussed yesterday in a different thread, problems like this frequently involve splitting a series of payments into two series, each of which you can evaluate. Here it is likely they did that, and then found it easier to evaluate at least one of them at time 8 than time 0. They could have used other splits, and could have chosen splits that did not require evaluation at time 8.
#3
11-05-2018, 08:38 AM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,039

Also, on the AO search is your friend. If you had searched the FM forum for “scholarship”, you would have found this thread, among others
http://www.actuarialoutpost.com/actu...d.php?t=114612 In it, no one suggested advancing to time 8, though they didn´t spell out a complete solution.

There’s also this one http://www.actuarialoutpost.com/actu...ad.php?t=54547, which does suggest considering time 8.

You could also search for Prescott and find those threads, and searching for names like that often gives you only results you care about, but then you wouldn’t pick up threads that didn´t include the donors name.
#4
11-05-2018, 11:31 AM
 Sullinator Member SOA Join Date: Aug 2018 College: West Chester Universiy Posts: 119

Quote:
 Originally Posted by Gandalf That quote is from a different thread, but same idea. Include your thoughts, and give people enough info. In FM, there are frequently multiple valid approaches, all ok, all giving the same answer. You didn´t even tell us what they did, and you expect us to tell us why they did what they did? As discussed yesterday in a different thread, problems like this frequently involve splitting a series of payments into two series, each of which you can evaluate. Here it is likely they did that, and then found it easier to evaluate at least one of them at time 8 than time 0. They could have used other splits, and could have chosen splits that did not require evaluation at time 8.
I’ll look it up thanks. I just suck at word problems.
#5
11-05-2018, 11:35 AM
 Colymbosathon ecplecticos Member Join Date: Dec 2003 Posts: 5,999

Quote:
 Originally Posted by Sullinator I just suck at word problems.
Then why would you be interested in a career that is essentially solving word problems full time?
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#6
11-05-2018, 11:36 AM
 Sullinator Member SOA Join Date: Aug 2018 College: West Chester Universiy Posts: 119

Quote:
 Originally Posted by Colymbosathon ecplecticos Then why would you be interested in a career that is essentially solving word problems full time?
I’ll get used to it I guess.

Last edited by Sullinator; 11-05-2018 at 11:42 AM..
#7
11-05-2018, 11:41 AM
 Sullinator Member SOA Join Date: Aug 2018 College: West Chester Universiy Posts: 119

Quote:
 Originally Posted by Colymbosathon ecplecticos Then why would you be interested in a career that is essentially solving word problems full time?
I mean people learn stuff they stink at, I’ll do the same I guess.
#8
11-05-2018, 02:49 PM
 Breadmaker Member SOA Join Date: May 2009 Studying for CPD - and nuttin' else! College: Swigmore U Favorite beer: Guinness Posts: 3,693

Key question: when does the first \$5,000 payment happen? Picking time 8 makes your life a little easier, no?
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#9
11-05-2018, 04:59 PM
 ShundayBloodyShunday Member CAS Join Date: Apr 2013 Posts: 2,176

Quote:
 Originally Posted by Sullinator I mean people learn stuff they stink at, I’ll do the same I guess.
Big difference between doing something as a means to continue doing what you enjoy vs. picking a career path based on something you aren't "good at".
#10
11-05-2018, 05:04 PM
 Sullinator Member SOA Join Date: Aug 2018 College: West Chester Universiy Posts: 119

Quote:
 Originally Posted by Breadmaker Key question: when does the first \$5,000 payment happen? Picking time 8 makes your life a little easier, no?
First 5000 happen at time 9, at time 8 it’s 4.5k, why does it make it easier? I know time 8 is the last time an increase happens, time 9 and after the payment stays at 5000, is that why?