C3: Premiums

[Smash Puny Human]

A 25 -year mortgage of 100K issued to (40) is to be repaid with equal annual payments at the end of each year. A 25 - year term insurance has a death ben which will pay off the mort. at the end of the year of death including the payment due. Given i =0.05, a(double dot)40:25| =14 and 25_q_40 =.2. What is the level annual ben premium for this term insurance. I think the answer is 435. (405, 414, 528 and 694 are the other choices). Thanks in advance.

[Gandalf]

Don't know about a formula, but Excel agreed with that result for at least one valid set of q's (0.005897 for first 24 years, to match annuity-due=14; then 0.077983 in year 25, to match 25q = 0.2).

Thus either 435 is right or the question is defective.

[ARCH]

I don't know a good direct way to do this one but here is one approach:

The value of the loan is 100,000 so using the calculator, the annual payment is 7095 (annuity-immediate). The person buying the insurance will make all the mortgage payments for as long as he lives so the value of his payments is V = 7095*(a(no dots)_40:25|) and the present value of the insurance has to be 100,000 - V since the term insurance makes any payments while (40) is dead.

To get at a(no dots)_40:25|, we can use the fact that it is the same as
a(double dots)_40:25| except for the first and last payment. so
a(no dots)_40:25| = a(double dots)_40:25| - 1 + 25_P_40 *v^25
= 14 - 1 + 0.23624 = 13.236.

So the actuarial present value of the payments while alive is
7095*13.236 = 93,909. So the APV of the Term insurance has to be 6091.

The level annual premium payment is 6091/a(double dots)_40:25| = 435.07.

This is kind of a hard problem.

[Double Down Trent]

I agree with ARCH, except for rounding. That is how Batten solved this very same problem yesterday in the NEAS Course 3 seminar, though he made it sound much easier than you ARCH.

[LosingInterest]

This last post is amusing to me. I know you've been around Bowden, but if Batten taught you some better way, then please enlighten us. Or did his methods not stick with you? I will not say I like either ARCH or Batten better, (although this post will make it seem like I back ARCH), but more-importantly I do take issue with your post. This person has taken the time to help and you've just ripped him whether intentionally or not. I understand this is a forum where one can vent however they please, but I personally will take comments like these with a grain of salt from you in the future. If there was an easier way, then why not share with us and make your point a useful one.

Regardless, I actually don't doubt it seemed alot easier at the seminar. And the reason it was easier at the seminar, something you seemed oblivious to by your post, is what amused me.

Fact is: You WERE at a seminar. I may very well be mistaken, but if it were anything like other seminars, this question and solution was most-likely presented in the context of other similar problems with discussions before and after relating to the topics used, and maybe even a couple of snazzy exhibits that might fall a little higher on the "teaching tools" scale than simple message board text. I'm sure I left some things out too.

Whereas, this was a stand-alone answer to a random problem posted on a message board, presented to us free of charge.

Just somethign to think about.