Actuarial Outpost Complex Annuities Practice
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 Financial Mathematics Old FM Forum

#1
10-31-2019, 06:50 PM
 Not Paul Member SOA Join Date: Mar 2019 College: St. Edwards University Posts: 132
Complex Annuities Practice

One of my weaknesses is complex payment schemes and timings so I've made one up.

Payments of 5 starting today made every other year for ten years followed by eight years of arithmetically increasing payments by 2 (7, 9, ect...) made yearly, all at 2% interest.

Does my equation for present value look correct?

$5\ddot{a}_{\overline{5}|4.04%} + [5\ddot{a}_{\overline{8}|2%} + 2(I\ddot{a})_{\overline{8}|2%} ]* v^{10}$
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Taking a well deserved break. Back at it in some capacity next year.

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Last edited by Not Paul; 10-31-2019 at 08:07 PM.. Reason: Removed the geometrically decreasing annuity to better focus attention.
#2
11-01-2019, 12:48 AM
 Academic Actuary Member Join Date: Sep 2009 Posts: 9,148

Your problem is ambiguous. Is there a one or two year interval from the final payment of 5 and the payment of 7?
#3
11-01-2019, 01:52 AM
 Not Paul Member SOA Join Date: Mar 2019 College: St. Edwards University Posts: 132

Hmmm... you're right. Two year interval.

Timeline where one dash is one year: 5--5--5--5--5--7-9-11-13-15-17-19
__________________
Taking a well deserved break. Back at it in some capacity next year.

P FM IFM
VEE: Economics VEE: Accounting VEE: Statistics
Job
#4
11-01-2019, 02:19 AM
 Academic Actuary Member Join Date: Sep 2009 Posts: 9,148

The formula looks correct but it is not the way I would solve it. I would solve for the present value at time 10 using the P,Q formula. Enter it into FV lets say with a negative sign. Enter -2000 PMT, 5 N, 4.04 I/Y and go to BGN mode. Then cpt PV. I normally don't like BGN mode because it is easy to forget you are in it but I think it works best in this case.
#5
11-04-2019, 01:44 AM
 Not Paul Member SOA Join Date: Mar 2019 College: St. Edwards University Posts: 132

Quote:
 Originally Posted by Academic Actuary I normally don't like BGN mode because it is easy to forget you are in it but I think it works best in this case.
Spoken like someone who used the ASM manual

Thanks for the engagement
__________________
Taking a well deserved break. Back at it in some capacity next year.

P FM IFM
VEE: Economics VEE: Accounting VEE: Statistics
Job