Solve the following equation:
50000=1000*a_bar_4*(1+i)^15 + 1000*s_10*(1+i) + 2000 * s_3 * (1+i) + X *
(Ia)_6* (1+i)^10
and I got X=286.89.
1) You have a continous annuity of paying 1000 from year 1 to year 4. The
accumulated
value of this is 1000*a_bar_4 * (1+i)^15, where the a_bar_4 is
(1-v^4)/delta
2) The second and third terms 1000*s_10*(1+i) + 2000 * s_3 * (1+i)
correspond to the steady
cash flow from end of year 5 to end of year 14.
3) The increasing annuity goes from the end of year 6 to the end of year
11.
4) Do remember that i =(1.05)^2-1.
Hope it makes sense and hope it is correct.
Good luck.
Doris
timothy.regan@zurich.com on 04/06/99 01:49:37 PM
To: studygroup4a <studygroup4a@lists.casact.org>
cc: (bcc: Doris Schirmacher/Re/Germany/Zurich)
Subject: Annuity problem
Help! No matter how many different approaches I use, I can't come up with the
given answer :
"An annuity has the following series of payments:
* $1,000 per year for the first 4 years payable continuously
* $1,000 starting at the end of the 5th year, increasing by X per year at
the end
of years 6 through 11
* $3,000 per year at the beginning of years 13 through 15
The nominal rate of interest is 10% compounded twice per year. The accumulated
value of the payments at the end of the 15th year is $50,000.
Determine X.
a.) Less than $295
b.) At least $295, but less than $305
c.) At least $305, but less than $315
d.) At least $315, but less than $325
e.) $325 or more "
The given answer is A.