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

 DW Simpson & CoWorldwide ActuarialRecruitment Entry Level JobsCasualty, Health, Life, Pension,Investment --Insurance / Consulting Asian JobsHong Kong, China, India, Japan, Korea, Indonesia, Singapore,Malaysia, and more Registration FormBe Notified of New Actuarial Jobs

#1
10-14-2007, 04:19 PM
 ewoj Join Date: Oct 2007 Posts: 5

QUESTION:Ralph buys a perpetuity-due paying 500 annually. He deposits the payments into a savings account earning interest at an effective annual rate of 10%. Ten years later, before receiving eleventh payment, Ralph sells the perpetuity based on an effective annual interest rate of 10%. Using the proceeds from the sale plus the money in the savings account, Ralph purchased an annuity due paying X per year for 20 years at an effective annual rate of 10%. Calculate X. [SOA 11/92 #4]
SOLUTION:
The solution is shown below but can someone explain to me how they wrote that equation for the ( MONEY IN THE SAVINGS ACCOUNT portion.. ie 500x1.1 divided by 0.1 part. i dont understand that portion of the equation.
Attached Images

#2
10-14-2007, 05:49 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 26,453

500*1.1/.1 = 500/d is the amount he sells the perpetuity-due for. The other piece is the money in the savings account.
#3
10-15-2007, 08:52 AM
 BadBeatMe Note Contributor SOA AAA Join Date: Jun 2007 Posts: 808

As Gandalf said, 500*1.1/.1 is the amount he sells the perpetuity-due for. Note that this is also what he paid for it, at the time of the sale he is selling a perpetuity-due of 500 annually which is exactly what he bought 10 years earlier.

The money in the savings account part, the left side, is simply the accumulated value of an annuity-due of 500 a year after 10 years. Since the money is coming from a perpetuity-due, the first payment is immediate, 10 payments are accumulated to immediately before the 11th payment, which is exactly what the FV of an annuity-due is.

Remember the formula for the PV of a perpetuity-immediate is 1/i. The reason the formula for the PV of this perpetuity-due is 500*1.1/.1 is the interest is 10% effective, the payment is 500 per year and we need to bring it forward a year because it is due, hence multiplying by 1.1.
#4
04-25-2013, 01:32 PM
 Felicia_lai Join Date: Jan 2013 College: Indiana University of PA Posts: 1

1. at the end of 10 years before the 11th payment recieved,
the saving is : 500 S (due angle n=10 @10%)
2. sell price is: 500/d
3. then the sum of that = X a (due angle n=20 @10%)
#5
04-25-2013, 02:30 PM
 ebeebs Member SOA Join Date: Jul 2008 Location: New England College: '09 grad Posts: 2,717

I'm verry curious why somebody registered in January and waited 3 months to make their first post on a thread from 2007.
#6
04-25-2013, 03:47 PM
 BruteForce Member SOA AAA Join Date: Apr 2013 Studying for FM - June, MLC - November College: Boise State University Favorite beer: Wurzel Bier Posts: 31

maybe they like to think before they speak... and I mean really think...
__________________
P FM

Und herein in schnellem Lauf Springt der Schneider in die Stub’ Zu dem Daumen-Lutscher-Bub. Weh! Jetzt geht es klipp und klapp Mit der Scher’ die Daumen ab, Mit der großen scharfen Scher’!
-Struwwelpeter
#7
04-25-2013, 07:12 PM
 actuary-r Member SOA Join Date: Nov 2012 College: Abilene Christian University '13 Posts: 90

Quote:
 Originally Posted by BruteForce maybe they like to think before they speak... and I mean really think...
__________________
P FM MFE MLC C

Take a free practice exam FM at http://actuarialinvestment.com/examfm.

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off

All times are GMT -4. The time now is 06:39 PM.

 -- Default Style - Fluid Width ---- Default Style - Fixed Width ---- Old Default Style ---- Easy on the eyes ---- Smooth Darkness ---- Chestnut ---- Apple-ish Style ---- If Apples were blue ---- If Apples were green ---- If Apples were purple ---- Halloween 2007 ---- B&W ---- Halloween ---- AO Christmas Theme ---- Turkey Day Theme ---- AO 2007 beta ---- 4th Of July Contact Us - Actuarial Outpost - Archive - Privacy Statement - Top