Actuarial Outpost
 
Go Back   Actuarial Outpost > Exams - Please Limit Discussion to Exam-Related Topics > SoA/CAS Preliminary Exams > Financial Mathematics
FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions


Financial Mathematics Old FM Forum

Reply
 
Thread Tools Search this Thread Display Modes
  #1  
Old 10-21-2018, 06:03 AM
Sullinator Sullinator is offline
Member
SOA
 
Join Date: Aug 2018
College: West Chester Universiy
Posts: 119
Default Problem

You are given an n-year annuity due of 1 per year plus a final payment at time (n+k-1). The present value of the payments can be simplified to (1-v^n+k)/d. Calculate the final payment.

Can someone please help me? Thank you.

Last edited by Sullinator; 10-21-2018 at 08:41 AM..
Reply With Quote
  #2  
Old 10-21-2018, 05:10 PM
Gandalf's Avatar
Gandalf Gandalf is offline
Site Supporter
Site Supporter
SOA
 
Join Date: Nov 2001
Location: Middle Earth
Posts: 31,044
Default

It would be helpful if you included the possible answers, if it is a sample multiple choice question, and what the source says the answer is.

Also, for the benefit of both you and people who might try to help you, you should start by posting your thoughts about how you might try to solve it. Biggest advantage of that: just documenting your thoughts may alert you to something youíre doing wrong or to how you could go further. Secondary advantage: no one has to document for you steps that you would already be doing on your own.

For this question, on reasonable approach (other thought processes would be similar):
1. What is the PV of all the payments except the last payment?
2. By subtracting that from the total PV, what is the PV of the last payment?
3. If thatís the PV of it, how much is the payment?
Reply With Quote
  #3  
Old 10-21-2018, 05:39 PM
Sullinator Sullinator is offline
Member
SOA
 
Join Date: Aug 2018
College: West Chester Universiy
Posts: 119
Default

((1+i)^(k)-1)/i is the answer but I don’t get it. I built a time line where I have payments of 1 at time 0, time 1, time n, n+k-1. Is that what I do?
Reply With Quote
  #4  
Old 10-21-2018, 06:30 PM
Gandalf's Avatar
Gandalf Gandalf is offline
Site Supporter
Site Supporter
SOA
 
Join Date: Nov 2001
Location: Middle Earth
Posts: 31,044
Default

Quote:
Originally Posted by Sullinator View Post
You are given an n-year annuity due of 1 per year plus a final payment at time (n+k-1). The present value of the payments can be simplified to (1-v^n+k)/d. Calculate the final payment.

Can someone please help me? Thank you.
Quote:
Originally Posted by Sullinator View Post
((1+i)^(k)-1)/i is the answer but I donít get it. I built a time line where I have payments of 1 at time 0, time 1, time n, n+k-1. Is that what I do?
Maybe sort of, but first clarify. Is post 1 supposed to say
Quote:
The present value of the payments can be simplified to (1-v^(n+k))/d
In any case, my suggestion (and this is certainly what the problem says), you build a time line with payments of 1 at time 0, time 1, ..., time n, then 0 at time n+1, n+2,..., then X at time n+k-1.
Then calculate the PV of the payments at payments of 1 at time 0, time 1, ..., time n. From that find out how much more you need as the PV of the payment of X.

What`s the source of the problem, and was it multiple choice?

As an aside (to help you understand why the answer is correct; not necessarily recommended because hard to see why you would do this under exam conditions). Think about a time line with payments of 1 at time 0, time 1, ..., time n, then y at time n+1, n+2, n+k-1. Get the PV of all those payments. Compare it to the PV of all the payments in your original series. Figure out how much y would be. Use that to figure out how much the single payment of X must be, to replace those payments of y you donīt get. Thatís not a recommended way to solve the problem. Itís just an ďah soĒ way of seeing why the answer works.
Reply With Quote
Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off


All times are GMT -4. The time now is 06:59 AM.


Powered by vBulletin®
Copyright ©2000 - 2019, Jelsoft Enterprises Ltd.
*PLEASE NOTE: Posts are not checked for accuracy, and do not
represent the views of the Actuarial Outpost or its sponsors.
Page generated in 0.15449 seconds with 11 queries