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

ACTUARIAL SALARY SURVEYS
Contact DW Simpson for a Personalized Salary Survey

Financial Mathematics Old FM Forum

Reply
 
Thread Tools Search this Thread Display Modes
  #1  
Old 02-23-2019, 07:47 PM
Mitsu96 Mitsu96 is offline
Member
Non-Actuary
 
Join Date: Jan 2017
Studying for IFM
Posts: 78
Default SOA Sample Question #85 and #101

SOA Sample #85

The present value of a perpetuity paying 1 every two years with first payment due immediately is 7.21 at an annual effective rate of i.
Another perpetuity paying R every three years with the first payment due at the beginning of year two has the same present value at an annual effective rate of i + 0.01.
Calculate R.

The answer is 1.74.

This is how SOA does it:

Name:  Screen Shot 2019-02-23 at 7.30.26 PM.jpg
Views: 210
Size:  10.8 KB

I got i = 0.077511 and j = (1 + i)^3 - 1 = 0.2861788. I used the following equation in order to find R,
(v^2)(a-dot-infinity)(R) = 7.21

With v = 1/1+j = 0.7774969

and I got R = 2.65384, which is definitely incorrect. I can't understand where I am going wrong the SOA's solution is not helpful either.
Any help is appreciated! Thank you!


SOA Sample #101

A 30-year annuity is arranged to pay off a loan taken out today at a 5% annual effective interest rate. The first payment of the annuity is due in ten years in the amount of 1,000. The subsequent payments increase by 500 each year.
Calculate the amount of the loan.

The answer is 64,257.

This is how SOA does it:

Name:  Screen Shot 2019-02-23 at 7.42.17 PM.jpg
Views: 204
Size:  10.5 KB

My only concern is why are there 30 payments? Shouldn't there by only 20 payments considering the first payment is due in 10 years (i.e., deferred annuity)?

Thank you for your help!
Reply With Quote
  #2  
Old 02-23-2019, 09:32 PM
morbrenn morbrenn is offline
Non-Actuary
 
Join Date: Nov 2018
Studying for the final finals
Posts: 10
Default

30-year annuity means the annuity lasts for 30 years. In this case, from the 10th to the 40th year.
__________________
P FM
Reply With Quote
  #3  
Old 02-23-2019, 09:49 PM
Academic Actuary Academic Actuary is offline
Member
 
Join Date: Sep 2009
Posts: 8,924
Default

For the first one, the beginning of year 2 is time 1 and the v should be at the one year rate.
Reply With Quote
  #4  
Old 02-24-2019, 05:41 PM
Mitsu96 Mitsu96 is offline
Member
Non-Actuary
 
Join Date: Jan 2017
Studying for IFM
Posts: 78
Default

Quote:
Originally Posted by morbrenn View Post
30-year annuity means the annuity lasts for 30 years. In this case, from the 10th to the 40th year.
Oh, so it's not a deferred annuity? It's just an ordinary 30 - year annuity?
Reply With Quote
  #5  
Old 02-24-2019, 05:42 PM
Mitsu96 Mitsu96 is offline
Member
Non-Actuary
 
Join Date: Jan 2017
Studying for IFM
Posts: 78
Default

Quote:
Originally Posted by Academic Actuary View Post
For the first one, the beginning of year 2 is time 1 and the v should be at the one year rate.
Got it! Thank you so much for your help!
Reply With Quote
Reply

Tags
annuity, financial mathematics, interest rate, perpetuity

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 08:02 PM.


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 0.14479 seconds with 10 queries