Sponsored Ads
Pauline Reimer, ASA, MAAA
Pryor Associates
Actuarial Openings: Life, P&C, Health, Pensions, Finance
Ezra Penland Actuarial Recruiters
Top Actuary Jobs
Salary Surveys Apply Bios Casualty Health Life Pension

Results 1 to 10 of 10

Thread: Annuity question

  1. #1
    Actuary.com - Level I Poster
    Join Date
    Oct 2010
    Posts
    19

    Exclamation Annuity question

    Hi,

    just wondering could someone help with this question on annuties. Here it is

    A loan made now is to be repaid by 99 daily repayments in arrear
    using an effective daily rate of 0.01%. The value of the repayments will
    alternate between 1,000 and 2,000 with the first of 1,000 to be
    paid in exactly one day's time.
    Find the current value of the loan.
    Last edited by Ronan1990; October 13th 2010 at 02:47 PM.

  2. #2
    Actuary.com - Posting Master
    Join Date
    Oct 2007
    Posts
    3,110
    Quote Originally Posted by Ronan1990 View Post
    Hi,

    just wondering could someone help with this question on annuties. Here it is

    A loan made now is to be repaid by 99 daily repayments in arrear
    using an e ective daily rate of 0.01%. The value of the repayments will
    alternate between e1,000 and e2,000 with the rst of e1,000 to be
    paid in exactly one day's time.
    Find the current value of the loan.
    So set up 2 annuities? Or one annuity of 1000 and then an incremental annuity every other year of 1000 as well.

  3. #3
    Actuary.com - Level I Poster
    Join Date
    Oct 2010
    Posts
    19
    Quote Originally Posted by NoMoreExams View Post
    So set up 2 annuities? Or one annuity of 1000 and then an incremental annuity every other year of 1000 as well.
    i set up 2 annuities and got my answer as 116372.28 but don't know if that's right

  4. #4
    Actuary.com - Level III Poster
    Join Date
    Sep 2010
    Location
    NY
    Posts
    130
    I set up the problem two different ways and arrived at an answer different than yours both times (I got the same answer both times, minus rounding errors).

    Realize the last payment of 2000 occurs at t=98 and the last payment of 1000 occurs at t=99.

    Approach 1: 1000a(angle 99 @0.01%) + 1000a(angle 49 @0.02%)
    *Note: the second annuity converts the interest periods to every two days and the new rate, j = 0.02% (solved by 1.0001^2 - 1)

    Approach 2: 1000a(angle 99 @0.01%) + 1000[ a(angle 98 @0.01%)/s(angle 2 @ 0.01%) ]
    *Note: the second annuity keeps the interest periods at daily

    Hope this helps.

  5. #5
    Actuary.com - Level I Poster
    Join Date
    Oct 2010
    Posts
    19
    Quote Originally Posted by NBran View Post
    I set up the problem two different ways and arrived at an answer different than yours both times (I got the same answer both times, minus rounding errors).

    Realize the last payment of 2000 occurs at t=98 and the last payment of 1000 occurs at t=99.

    Approach 1: 1000a(angle 99 @0.01%) + 1000a(angle 49 @0.02%)
    *Note: the second annuity converts the interest periods to every two days and the new rate, j = 0.02% (solved by 1.0001^2 - 1)

    Approach 2: 1000a(angle 99 @0.01%) + 1000[ a(angle 98 @0.01%)/s(angle 2 @ 0.01%) ]
    *Note: the second annuity keeps the interest periods at daily

    Hope this helps.
    Ok thanks for that it does help, i think the two I was setting up were wrong I said the first annuity was 1000a(angle 50 @ 0.01%) and i added this onto 2000a(angle49 @ 0.01%), could you do it this way or is there something wrong with it?

  6. #6
    Actuary.com - Level III Poster
    Join Date
    Sep 2010
    Location
    NY
    Posts
    130
    What you have written is a present value of a 49 term annuity with payments of 3000 and an additional payment of 1000 at t=50. So yes, there is something very wrong with it.

  7. #7
    Actuary.com - Level I Poster
    Join Date
    Oct 2010
    Posts
    19
    Quote Originally Posted by NBran View Post
    What you have written is a present value of a 49 term annuity with payments of 3000 and an additional payment of 1000 at t=50. So yes, there is something very wrong with it.
    yeah but if there's 99 repayments in total, and it alternates between 1000 & 2000 should that not mean you're dealing with an annuity of 1000 for 50 time periods and 2000 for 49 time periods??

  8. #8
    Actuary.com - Level III Poster
    Join Date
    Sep 2010
    Location
    NY
    Posts
    130
    No. Remember annuities discount the payments to present value. So the payment stream looks like:

    PV = 1000v + 2000v^2 + 1000v^3 + ... + 2000v^98 + 1000v^99

    What you have written is:

    PV= 1000v + 2000v + 1000v^2 + 2000v^2 + ... +1000v^49 + 2000v^49 + 1000v^50
    = 3000v + 3000v^2 + .... + 3000v^49 + 1000v^50.


    I hope that helps. If you are confused with annuities, write out the payment stream.

  9. #9
    Actuary.com - Level I Poster
    Join Date
    Oct 2010
    Posts
    19
    Quote Originally Posted by NBran View Post
    No. Remember annuities discount the payments to present value. So the payment stream looks like:

    PV = 1000v + 2000v^2 + 1000v^3 + ... + 2000v^98 + 1000v^99

    What you have written is:

    PV= 1000v + 2000v + 1000v^2 + 2000v^2 + ... +1000v^49 + 2000v^49 + 1000v^50
    = 3000v + 3000v^2 + .... + 3000v^49 + 1000v^50.


    I hope that helps. If you are confused with annuities, write out the payment stream.
    oh right I see what i've been doing wrong now thanks, but one more question. Take your approach 1...are you saying the PV is (1000v +1000v^2+...1000
    v^99) + (1000v + 1000v^2....1000v^48)??

  10. #10
    Actuary.com - Level III Poster
    Join Date
    Sep 2010
    Location
    NY
    Posts
    130
    No. Note that I converted the interest period to 2 days, instead of 1 day. This means that payments will occur at the end of every even day.

    This question tests your ability to calculate the present value of annuity where payments occur less frequent than the interest period. You have two options: (a) convert the interest period to the payment period or (b) use the original interest period. Option (b) requires you to know that if payments occur every k periods over n interest periods, the present value of the annuity immediate evaluates to a(angle n) / [s(angle k).
    Last edited by NBran; October 25th 2010 at 10:19 AM.

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Similar Threads

  1. immediate annuity question clarification
    By liltich in forum SOA Exam FM / CAS Exam 2 - Financial Mathematics - with practice exam problems
    Replies: 2
    Last Post: October 7th 2009, 01:08 PM
  2. Annuity and Loan question - Please help
    By navya in forum SOA Exam FM / CAS Exam 2 - Financial Mathematics - with practice exam problems
    Replies: 6
    Last Post: November 6th 2007, 01:26 PM
  3. Annuity Question
    By atabd in forum SOA Exam FM / CAS Exam 2 - Financial Mathematics - with practice exam problems
    Replies: 2
    Last Post: May 23rd 2006, 05:51 AM
  4. Annuity question
    By hristov in forum SOA Exam FM / CAS Exam 2 - Financial Mathematics - with practice exam problems
    Replies: 5
    Last Post: May 12th 2006, 04:42 PM
  5. annuity question.
    By audia4 in forum SOA Exam FM / CAS Exam 2 - Financial Mathematics - with practice exam problems
    Replies: 2
    Last Post: September 22nd 2005, 03:56 AM

Tags for this Thread

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •