C2: TOI

[shluffer]

The temple manual, sample exam 2 question 17:

Kimberley is told that she can receive a $250,000 death benefit from her husbands life insurance policy in annual installments of 25,000 at the beginning of each year for 11 years and a final payment of 16265 at the beg. of the 12th year. Or, she can receive 13,000 at the beg. of each year for life, with a certain period of 10 years. Calculate the PV of a 10-year deferred life annuity due of 1 per annum at Kimberley’s age.

I can answer the question, I'm just wondering if it is on the syllabus. :-?

[c3 taker]

The temple manuel, sample exam 2 question 17:

Kimberley is told that she can receive a $250,000 death benefit from her husbands life insurance policy in annual installments of 25,000 at the begining of each year for 11 years and a final payment of 16265 at the beg. of the 12th year. Or, she can receive 13,000 at the beg. of each year for life, with a certain period of 10 years. Calculate the PV of a 10-year deffered life annuity due of 1 per anum at kimberley's age.

I can answer the question, I'm just wondering if it is on the sylabis. :-?

I think that this question is definately fair game for the exam. The only questionable thing is 10-year deferred annuity due but I think you should know what that is. I wouldn't be surprised to see a question like this on the exam.

[retaker]

Are you sure?

That wouldn't be very nice.

[shluffer]

I don't think it is covered because the question requires a mortality asumption. The answer is computed without mortality (just use x as your n for the anuity) but the question requires knowledge of how to deal with mortality which is a very basic Life Contingencies concept but still a LC concept.

[retaker]

Exactly

[Mardi]

Not really. You can calc the PV of the certain stream and set it equal to 13000X where X is that annuity payable at 1 per annum. No mortality yet.

If you have to find a piece of the annuity, or actually figure out her age, it would be different. But I don't read that into this question.

[MathGuy]

Calculate the PV of a 10-year deffered life annuity due of 1 per anum at kimberley's age.

The problem explicitly asks for the value of a life annuity dependent upon Kim's age. This is not covered on exam 2. Therefore, the question could not be asked. If the problem were reworded to state something like, "assuming she does not die", then it would be a valid course 2 problem, but in that case they would instead remove the references to a life annuity and her age.

[Mardi]

no, MG, actually this is just like the SoA to give the impression you need it. They add extraneous info to other questions to throw you off. It's just a PV = PV problem.

[fallout]

The temple manual, sample exam 2 question 17:

Kimberley is told that she can receive a $250,000 death benefit from her husbands life insurance policy in annual installments of 25,000 at the beginning of each year for 11 years and a final payment of 16265 at the beg. of the 12th year. Or, she can receive 13,000 at the beg. of each year for life, with a certain period of 10 years. Calculate the PV of a 10-year deferred life annuity due of 1 per annum at Kimberley’s age.

I can answer the question, I'm just wondering if it is on the syllabus. :-?

I think it can be on course 2.

Use the first part of the problem to solve for i,

plug I into the the second part to solve for n.

250,000 =13000(annuity due 10, i)+13,000(annuity due deferred 10, n, i)

solve for (annuity due,n,i)

You don't need any mortality knowledge.

There was a similar question such as: Mr. Jones can buy a $1,000 per month for life starting at age 65 for $213,000. (I made up the numbers and the names, but it is in part 2 for May 2002).

[OldFSA]

There is one reason that we can be certain that this could be asked on an interest theory actuarial exam from the SOA.

It was.

[retaker]

I am sure they have or would ask this type of question, but it seems questionable to do so.

Maybe I have forgotten my life contingencies, but isn't the equation:

Solve for i as fallout said, then:

250,000= 13,000a_10(no life) + (10_E_x) * a_(x+10)

They ask for the second term on the right. A 10-year deferred live contingent annuity. If you have not studied life contingencies you may not know how to for the above equation and hence may not know to simply compute the 10 year certain annuity at the interest rate you solved for and then subtract it from 250,000 to get the answer

[retaker]

Sorry

250,000= 13,000[a_10(no life) + (10_E_x) * a_(x+10)]

[MathGuy]

OldFSA: When was this on an exam?

I agree that the mortality data is not needed to solve the problem. I checked the syllabus for exam 2, and it never states explicity that that only annuities-certain are included in the exam. However, if I recall correctly, Kellison only addresses annuities certain. I believe one of the sections in Kellison is called "Uncertain time" and is excluded from the syllabus.

Consider fallout's solution:

250,000 =13000(annuity due 10, i)+13,000(annuity due deferred 10, n, i)

What basis does a course two student have for writing such a formula, which is technically wrong, because it calculates the value of an "annuity due deferred" with n payments, which is an annuity certain, whereas the question asks for the value of a life annuity. Although he gets the correct answer, his solution is wrong.

[retaker]

I couldn't tell what he was trying to say.

How does a 10 -yr deferred annuity certain for n years get in the picture?

[MathGuy]

retaker, the thing is that if you write the equation as

250,000 =13000(annuity due 10, i)+13,000*ELEPHANT

and solve for ELEPHANT, you get the correct answer. The question is, and I think you were implying this, would a course 2 student know that a life annuity with a ten year certain term is the same as a ten year annuity certain plus a ten year deferred life annuity (or, in this case, an elephant)? I think it's highly unlikely, given that they've never seen a life annuity before.

[retaker]

Exactly what I was trying to say.

On a different note, technically for this particular problem there is only one particular elephant which is correct, namely:

(10_E_x) * a_(x+10)

[shluffer]

The question was asked on an exam where LC was on the sylabus. I would suggest that if the question was reworded to state that Kim lives to age x, you would no longer be able to say that it is a LC question. I don't think a certain annuity is on the sylabus though.

[retaker]

I reconize that lyric Math Guy, where is it from?

[OldFSA]

Shluffer, MathGuy, etc.

I am not in any way trying to justify that this question should have been on an SOA Interest Theory Exam; it probably should not have been.

However, it WAS Question #17 on the Fall 1989 SOA Course 140 Exam, an exam which had absolutely neither life contingencies content nor life contingencies prerequisite. There was considerable discussion among actuarial students at the time about the question, much of which could have been categorized as irate, as you might imagine.

[MathGuy]

retaker: bnl, "Helicopters"

[retaker]

Okay, maybe I don't remember hearing it. What is bnl?

[MathGuy]

barenaked ladies http://www.azlyrics.com/lyrics/barenakedladies/helicopters.html

[Steve White]

Exactly what I was trying to say.

On a different note, technically for this particular problem there is only one particular elephant which is correct, namely:

(10_E_x) * a_(x+10)

I don't think the problem would be appropriate for Course 2 or was appropriate for 140 in 1989. If the candidates had to recognize that product, it is far outside Course 2. In fact, all they need to recognize is that the life annuity due with 10 years certain is the sum of the 10 year certain annuity and the 10 year deferred annuity. That still seems like too much to expect.

[Summer]

we had to know basic economic theories for course 1, which i didn't know until i started writing the practice exams

eg. Profit=revenue*amount
and things like that

(elasticity of demand was on quite frequently, although they gave us the formulas for that, so I guess it wasn't something we were expected to know)

My point? If we were expected to know some basics from course 2 for course 1, as long as solving the problems were using course 1 material, doesn't it stand to reason that it is possible we have to know some basics from course 3 for course 2, as long as solving the problems are using course 2 material?

[Steve White]

The standard should be "what is basic knowledge?". If the Course 1 committee tests on the knowledge that "Profit = Revenue * amount", it should be with the expectation that virtually everyone knows it, not that people should have read Course 2 material. I would be mildly surprised if they even required that much. but something like Total sales = sales volume * price per unit would strike me as clearly fair.

Why would the course 2 committee expect the candidate to know that a life annuity with ten years certain is equivalent to a ten year certain annuity plus a ten year deferred life annuity? To me, it is unreasonable to expect that most people would know it in the absence of any actuarial/insurance education. It is unreasonable to expect that the course 2 candidate knows it from course 3.

[fallout]

Course 2 syllabus includes adding and subtracting annuities does it not?

Could they not say give you a 10 year annuity and a 10 year deferred 10 year annuity and ask you the price of a 20 year annuity?

[MathGuy]

In order to solve this problem, a course two taker would need to know/assume that you can add the values of a 10-year annuity certain and a 10-year deferred life annuity to get the Present value. A course three student would know this (in theory), but a course two taker would not. If a student has never read about life annuities before, they would have no reason to think this is true. "What if she dies before ten years are up?" they may ask themselves. They shouldn't have to guess.

Here is all the material on life annuities contained in the course 2 syllabus:

"A common type of contingent annuity is one in which payments are made only if the person is alive. Such an annuity is called a life annuity. For example, monthly retirement benefits from a pension plan, which continue for the life of a retiree, constitute a life annuity.

"In this book, we will largely restrict our attention to annuities-certain. However, the risk of default or non-payment is addressed in Section 9.5. It will often be convenient to drop the word 'certain' and use the term annuity to refer to an annuity certain."

This is from the beginning of chapter 3. Note that Section 9.5 is not on the syllabus and that annuities-certain are consistenty referred to as "annuities" in the book and in the exams, suggesting that there is no need to differentiate.

[VernSchil]

Before one even arrived at adding the two annuties together, how would a course 2 taker even know how to calculate a 10 year deferred life annuity? Don't you need to use N's and D's for that? ( N(x)/(D(x-10) )?

[Steve White]

If you think that the course 2 candidate should recognize that the total life annuity (with certain period) is the sum of the two pieces, they don't need to know the formula for the deferred annuity. They know the value of the total life annuity (with certain period), and they should know how to calculate the value of the certain piece. So the value of the deferred life annuity is the difference.

Many would not agree that course 2 candidates must know that the total life annuity is equal to the sum of those pieces.