

FlashChat  Actuarial Discussion  Preliminary Exams  CAS/SOA Exams  Cyberchat  Around the World  Suggestions 
DW Simpson Global Actuarial & Analytics Recruitment 
Financial Mathematics Old FM Forum 

Thread Tools  Search this Thread  Display Modes 
#1




Annuities Question (ACTEX M2  76 #6)
The problem
To accumulate 8000 at the end of 3n years, deposits of 98 are made at the end of each of the first n years and 196 at the end of each of the next 2n years. The annual effective rate of interest is i. You are given (1+i)^n = 2. Determine i. My timeline Let a = 98 and b = 196 aaaabbb000 0123 ... nn+1n+2...2n2n+12n+2...3n My reasoning A series of payments of 98 is followed by a series of payments of 196. Payments are stopped and everything in the bank earns interest for n years. The accumulated value at the end of 3n years is 8000. (98s_n + 196s_2n)(1+i)^n = 8000 The actual solution The solution says payments continue on to the end of 3n years. A series of 98 payments is made for 3n years and a second series of 98 payments begins at n+1 years and continues until the end of 3n years. 98s_3n + 98s_2n = 8000 What I don't understand Why are payments taking place between 2n and 3n years? In general I am having a very difficult time setting up problems involving annuities. While I've got a much better handle on the formulas and vocabulary than I did last month I am still coming up short when trying to set up the problems. Any suggestions for tackling annuities in general?
__________________
Taking a well deserved break. Back at it in some capacity next year. VEE: Economics VEE: Accounting VEE: Statistics Job Last edited by Not Paul; 08012019 at 02:37 PM.. 
#2




and 196 at the end of each of the next 2n years

#3




Also, you neglected the investment income from years 1 through 2n.
__________________
"What do you mean I don't have the prerequisites for this class? I've failed it twice before!" "I think that probably clarifies things pretty good by itself." "I understand health care now especially very well." 
#4




at the end of each of the next 2n years.
So what your saying is n + 2n = 3n? Well that's obvious now
__________________
Taking a well deserved break. Back at it in some capacity next year. VEE: Economics VEE: Accounting VEE: Statistics Job Last edited by Not Paul; 08012019 at 06:34 PM.. Reason: Because frustordom (boredom and frustration) 
#6




8000 = 96s_n*(1+i)^2n + 192s_2n = 96s_3n + 96s_2n (Evaluation at time t=3n)
__________________
"What do you mean I don't have the prerequisites for this class? I've failed it twice before!" "I think that probably clarifies things pretty good by itself." "I understand health care now especially very well." 
Thread Tools  Search this Thread 
Display Modes  

