Course 5 Savings Rate Question

[pbj]

Does anyone remember their answer to this? I think I got 5.55% or something close to that. Some of the details I remember are that current salary was 80K, salary scale was 3%, saving return was 7%, social security was 11,700, and the retirement ratio was 70%.

[MG]

That sounds like what I got - I think I ended up with 5.565% as my answer.

[Anonymous]

I got about 5.9 percent. I think that this is due to the fact that I assumed that each savings contribution went in at the end of each year. You probably assumed that the savings went in at the beginning of each year.

Can you confirm?

[pbj]

I hadn't thought about timing but now that I do, I did assume contributions at the beginning of the year.

[Relaxed]

How did you finish that problem? You calculate what he needs to have saved at retirment, but how do you get the percent? I'm thinking you get the last payment by calculating an anuity at interest rate (1+i)(1+s)-1. Is that right?

<font size=-1>[ This Message was edited by: Relaxed on 2001-11-01 15:27 ]</font>

[WWSituation]

OK, 24 hrs since the exam. Here we go:


My answer was about 11.5%.

I double checked it backwards and forwards. I assumed beginning of year contributions (so what!)

You must divide by the annuity at (1.05)/(1.03) -1 interest rate.

[Anonymous]

It's the sum of a geometric progression buddy.

[The Bomb]

I also got somewhere near 5.565%. My final equation ended up being something like:

400,000 = 80,000 * (X%) * {(1.07)^25 + [(1.07)^24 * (1.03)] + [(1.07)^23 * (1.03)^2] + ... + [(1.07) * (1.03)^24]}

I didn't know how to evaluate the expression in the brackets, and since I had like an hour to kill, I just calculated all 25 terms and got the answer posted above.

But, if I get even a 1 on this thing, I'm gonna be shocked out of my socks, so don't place any realistic amount of merit on my answer. :smile:

[Not Mike]

Grayspring, that's what I thought (I forgot how to solve it) and I ended up with a factor of:

Summation [(1+i)^t * (1+s)^(25-t)] summed from t=0 to 24

That Summation times 80,000 should be set equal to the amount that you need at retirement, I believe....

[ajphilly]

I got 11.65% too. I solved it like a accummulated annuity due.

[aNoNo]

Did anybody think about projecting the Social Security benefit to age 65 so that the percentage of pay replaced by Social Security would remain constant from age 40 to age 65?

[ACCtuary]

You forgot that 90% of your accumulated assets in this fund are to be deducted as a fee to the Dogbert Deferred Earnings Fund. It was not stated in the problem, but it should have been assumed.

I wish I had said something silly like that on the test. Poor graders are sitting alone in a hotel suite in Vegas with nothing but expensive escorts for company :wink:



<font size=-1>[ This Message was edited by: AntiEverything on 2001-11-01 15:54 ]</font>

[The Bomb]

Since I was already assured of a "Fail", I did "let loose" a little in the afternoon session.

When asked to describe taxation in Canada, I simply wrote:

"I don't know much about Canada, other than they've got good beer, and that it's really cold. Perhaps I should study this section a little more thoroughly next time, eh?"

I figure...if I'm gonna get a zero, at least I can hope that the grader is making that big red O with a smile on his/her face.

[Anonymous]

Response to WWSituation:

I believe you're right. This is how I did it.

<font size=-1>[ This Message was edited by: Tim on 2001-11-01 16:08 ]</font>

[The Bomb]

Just out of curiosity, Tim, to whom is the following directed?

I believe you're right.

Just thought I'd ask...

[Anonymous]

To The Bomb:
I responded to WWSituation. I hope I'm right.

[Relaxed]

I think I got a 10.9%. I did the (1+i)/(1+s)-1 interest rate thing. But that doesn't make sense to me anymore. Does that work out to the same thing as the Not Mike/Bomb progression thing? Is the difference whether you divide by the starting salary or the ending salary?

I hate first principles.

[Anonymous]

The theory of interest book has a different formula (p 85). But exercise 3.10 of the pension funding and valuation book uses the formula that WWSituation stated. I haven't bothered to reconcile the two formulas.

[Relaxed]

LOL Bomb!!! The "Eh" was a particularly nice touch.

[fsa2be]

we were given salary at age 64 and it wasn't what you would have expected it to be so I question the correctness of your summation from 0 to 24 Not Mike.

[ajphilly]

80,000 * 1.03^24 = 162,624. I believe this is the salary they gave us at age 65.

[Anonymous]

What was the pension benefit formula? I think it was based on a final 3-year average.

[Snow White]

[Snow White]

Oops. Am I ever stupid today.
I also checked the 80,000 increased to age 64 and I concurred with their answer. I did the summation method and am pretty confident about it. Got around the 5. something answer.

[The Bomb]

If I recall correctly, the pension benefit was 1% of 3-Year Average of Final Salary per year of service (and I don't remember how many years of past service he had in addition to the 25 yrs of service from Age 40 to Age 65).

[Not Mike]

I did it in Excel today using the progession and came up with approx 5.56% using 80,000 as the starting salary and 397,000 as the amount needed at retirement (I think I got 396,996 or something like that on the exam)....

[ajphilly]

I think the answer is around 5 too but I don't understand why 1.07/1.03 -1 interest rate for an accumulated annuity is the wrong method (gives 11.5%). First principles has that the answer should be around 5.

Anyone have any insight?

[The Bomb]

396,996 is my exact amount as well--funny how I remembered that! :smile:

[The Bomb]

Ok, I spoke with a really smart person in my office, and she suggested that to solve for X in my formula from my previous post:

400,000 = 80,000 * (X%) * {(1.07)^25 + [(1.07)^24 * (1.03)] + [(1.07)^23 * (1.03)^2] + ... + [(1.07) * (1.03)^24]}

one can multiply through by (1.03)^25 / (1.03)^25, which would give you:

80,000 * (X%) * (1.03)^25 * {(1.07 / 1.03)^ 25 + (1.07 / 1.03)^24 + .... + (1.07 / 1.03)}

The expression in the { } reduces to [(1.07 / 1.03)^25 - 1] / [(1.07 / 1.03) - 1].

Solving it this way gives me X% = 5.78%

But, again, I don't have a buttload of confidence in my methodology...

[ajphilly]

You got the right answer. That looks right.

[Anonymous]

Right or wrong, if the methodology up to that point is right, we'll get most of the points

[pbj]

The way I solved for the interest rate was to write out a few of the terms ...
80,000*U*(1.07)^25 + 80,000*(1.03)*U*(1.07)^24+...+ 80,000*(1.03)^24*U*(1.07).
Somehow I decided that this equaled 80,000*U*("s-bracket-25" at rate j)*(1.07)^25 where j = (1.03/1.07 - 1) Yes I know that makes j negative, but it seemed to equal all the terms I wrote out. I got the 5.5% answer

[Relaxed]

Is it a coincidence that EndingSalary/StartingSalary = 11.5%/5.5%?

After you get an anuity payment amount using (1+i)/(1+s)-1 as interest, you get the popular answer if you divide that payment by the ending salary.

[Anonymous]

AJPhilly-

I believe the reason it does not work is that the accumulated annuity formula assumes that the payments are accumulated at the interest rate 1.07/1.03-1 = 3.88%, when in fact, the payments are accumulated at the full interest rate of 5%. I think this accounts for the difference between the 5.6% answers and the 11.5% answers.

[Anonymous]

Make that "full 7% interest rate".

[Anonymous]

Does anyone recall the given annuity factor at age 65?

[ajphilly]

i think it was around 8.9 or something.

[Transdermal Celebration]

I think the annuity factor at age 65 was 8.12

As for the US-Canada problem, I reference the (face - 50,000)x Table I Rate - (ee contributions) formula for group term life insurance taxation... think I'll get 1 point for that?
For the Canada part, I just repeated what I wrote for the US part, and put "eh" at the end of each answer. A happy grader I think is in my best interests, as long as s/he isn't canadian.

good luck to all and to all a good night.

[smarty pants]

This was brought up in another thread with no conclusion. Wasn't Replacement Ration defined in the study note to be (Retirement Benefit + SS Benefit)/Pay at retirement? I know it doesn't make sense for this problem and pay replacement should take into consideration all post retirement monthly income plans. My problem is that I accidentally left out the SS portion and did the rest correctly from that point. Any idea on how brutal they'll be to me?

[Health guy]

The way I solved this problem is to look at the savings as being similar to the normal cost contributions under ILP with level %. Using this method, I calculated the NC(sub40) then using 80,000 as the salary, solved for NC=U*S. This gave me 5.56%

[RBF]

As for the US-Canada problem, I reference the (face - 50,000)x Table I Rate - (ee contributions) formula for group term life insurance taxation... think I'll get 1 point for that?

Funny, I think that's about all I knew too.

[Anonymous]

Anyone confirm the annuity factor given? 8.1894?

[Anonymous]

Does it really matter what the annuity rate was?

The test is over. Wait for the results.

[RBF]

On 2001-11-02 11:00, Mitch Comesteen wrote:
Anyone confirm the annuity factor given? 8.1894?


it was 8.1958

[Phil]

I thought the annuity factor was 8.9185. At any rate, I agree with RBF that the digits after the decimal point were 1,5,8, and 9.

The replacement ratio problem specifically said "full replacement ratio", and I assume that is their roundabout way of telling us to include Soc Sec benefits.

[WWSituation]

I think it goes without saying that Social Security would be included.

It is standard for industry practice to include it. If you didn't include it, I hope you disclaimed it with something like

"Although Social Security is an important part of the traditional 3 legged stool of retirement income that we studied in a multitude of different sources for this exam, I am choosing to ignore it here - even though you have made it painfully easy for me to include it by simply giving me the annual value and relieving me of having to do the ridiculous calculation on my own

[Ponderer]

Now that the exam is posted and that we are off the exam pressure, I tried to solve this problem again and I got 7.33%. I screwed up on the actual exam (or maybe still do) where I calculated the percent of salary (using the present value approach) based on the benefit = (70% * 162,624) - 11,700 which, now I think should have been (70% * 162,624) - 11,700 - 38,329, the last component being the portion of retirement benefit that is funded by the pension scheme in addition to the personal savings, i.e. B_sub_65 = 38,329. Note the word "retirement benefit" when the problem describes the B_sub_65, which I now think possibly implies a source of retirement income from a private pension scheme. I did not interpret the problem that way when I was writing the exam because I totally did not see it coming, i.e. it incorporates not only the personal savings, but also the government-sponsored security benefit, AND possibly the employer-sponsored pension benefit. There! Now we have all the 3 legs of a stool! Anyone agree with me? And I thought this was easy back then!

Sigh... Looks like my chances of passing this exam on first attempt like I did with the previous math exams are much slimmer now... But then again I guess I won't regret too much because work had been crazy a month going into the exam period and I only got to study around 200 hours for this sitting (200 hours cut it for me with courses 3 and 4 though).

<font size=-1>[ This Message was edited by: Ponderer on 2001-11-07 03:44 ]</font>

[smarty pants]

This isn't course 3 or 4 though. Muy dificil.

[Axsuetarian]

Hey Ponderer,

Just because you got the ANSWER wrong on one question, does NOT mean you failed the exam, never mind, you may of still got full marks on that QUESTION

I wouldn't start studying for next Nov just yet!

More important then the numerical questions, was your ability to spit out the appripriate lists and relevant sub points for the 80% of the written answer piece that was "list only" essentially

Hang in there buddy,

[Ponderer]

Thanks for the words of encouragement. I totally skipped questions #9 and #10 in the afternoon as a result of my study strategy - skipping country-specific material and stuff that was on last year's exam given the limited time I had. So that's like another 11 points gone into the drain... And then there was a whole bunch of MC questions that are country-specific. I estimated rather optimistically my total points to be somewhere around 55. I guess I'm sort of at the borderline between passing and failing huh?

Strange that in all the previous posts on this savings problem, none has talked or thought about the way I interpret this problem. Could I be wrong in my interpretation?