Actuarial Outpost HELP WITH ANNUITY OFF-PAYMENT NUMERICAL APPROACH
 Register Blogs Wiki FAQ Calendar Search Today's Posts Mark Forums Read
 FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

 Enter your email to subscribe to DW Simpson weekly actuarial job updates. li.signup { display: block; text-align: center; text-size: .8; padding: 0px; margin: 8px; float: left; } Entry Level Casualty Health Life Pension All Jobs

 Financial Mathematics Old FM Forum

#1
10-11-2017, 04:12 PM
 klink SOA Join Date: Sep 2013 College: UW- River Falls Posts: 5
HELP WITH ANNUITY OFF-PAYMENT NUMERICAL APPROACH

For the life of me I cannot figure out how to get an answer using numerical approach. I have reread Section 4a to 4c over and over.

Question 1: 100 deposited at the beginning of each 4-year period for 40 years. Account credits annual effective interest i. Accumulated amount at end of 40 years is X which is 5 times accumulated amount at the end of 20 years.

I set up using 4 year payment period with effective interest j=((1+i)^4)-1

Setting (using interest j): 500(s angle 5) = 100(s angle 10), I get j=31.95%.
From j, i=7.18% which is what the solutions show.

When I try to find X @ j=31.95%, i use: X=100(s angle 10)= 4701.52

The correct answer is supposed to be 6195.

The solution shows the symbolic approach setting up the problem as:
100(s angle 40/a angle 4)=500(s angle 20/a angle 4) which also yields i=7.18%

Then they use X=100(s angle 40/a angle 4) @ i=7.18%, X=6195

Please help me figure out where I am going wrong when trying to solve for X using the numeric approach!!!!!!!!!!!!!
#2
10-11-2017, 04:30 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,226

Payments are beginning of each interval so double dot the s's. Also your 4701.56 should be 4694.53, the multiply by 1.3195.