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 12-03-2018, 10:47 PM
dws098 dws098 is offline
Non-Actuary
 
Join Date: Nov 2018
Posts: 2
Default FM exam question - annuity with varying interest rates

Question: Five deposits of 100 are made into a fund at two-year intervals with the first deposit at the beginning of the first year.
The fund earns interest at an annual effective rate of 4% during the first six years and at an annual effective rate of 5% thereafter.

Calculate the annual effective yield rate earned over the investment period ending at the end of the tenth year.

____________________________

Approach: I set up an equation to calculate the present value:

PV = 100 + 100(1.04)^(-2) + 100(1.04)^(-4) + 100(1.04)^(-6) + 100(1.04)^(-6) * (1.05)^(-2).

I get that the present value is 428.65, that is 428.65 = (a_5) * (1+i), where i is the two-year effective interest rate. Solving with linear interpolation, I get 8.35% for the two-year effective interest rate meaning the effective annual interest rate is 4.09%. But the solutions manual gives 4.58% as the correct answer, where they set up the accumulated value as follows:

AV = 100(1.04)^6 * (1.05)^4 + 100(1.04)^4 * (1.05)^4 + 100(1.04)^2 * (1.05)^4 + 100(1.05)^4 + 100(1.05)^2. This gives 659.27 as the accumulated value (and the annual effective interest rate would indeed be 4.58%).

Both my solution and the one in the answer key should make sense, yet they give different values for the effective interest rate. What am I doing wrong?
Reply With Quote
  #2  
Old 12-03-2018, 11:13 PM
Gandalf's Avatar
Gandalf Gandalf is offline
Site Supporter
Site Supporter
SOA
 
Join Date: Nov 2001
Location: Middle Earth
Posts: 31,039
Default

You need to work with accumulated values, because the question asks about the 10 year period.

Your method would give the same answer if the interest rate in years 9 and 10 were 5% (as it is) or if the interest rate in years 9 and 10 were 20% (or 0%, or 4%, or anything)

Your method (slightly modified) would work if you made a total withdrawal of the accumulated value at the end of 10 years, and then solved for the interest rate that would make the PV of all the deposits and the withdrawal 0.
Reply With Quote
  #3  
Old 12-03-2018, 11:51 PM
dws098 dws098 is offline
Non-Actuary
 
Join Date: Nov 2018
Posts: 2
Default

Interesting, thanks.
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 08:46 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 1.72379 seconds with 9 queries