Ch18 Practice Questions 18.6 vs 18.10(iii)(c)

[Brett Kim]

This is in regard to the end of chapter questions for Chapter 18.

From what I can understand, questions 18.6 and 18.10(iii)(c) are essentially the same question with different compounding and interest rates. However, I don't understand why the equation of the death benefit component of the EPV are different.

To explain further, the solution for 18.6 works from first principle so I can see how we arrive at 25,000 * 1.066^(0.5) * <term assurance of a 48 year old with a term of 17 years evaluated at 4% interest>.

So if I do the same and work from first principle for 18.10(iii)(c) I arrive at 100,000 * 1.08^(0.5) * <term assurance of a 45 year old with a term of 20 years evaluated at 4% interest>. But the solution uses the claims acceleration approximation of an assurance paid immediately, hence getting 100,000 * 1.04^(0.5) * <term assurance of a 45 year old with a term of 20 years evaluated at 4% interest>.

What am I misunderstanding here?

My working for 18.10(iii)(c) from first principle:
https://imgur.com/iAcGfJP

 

[Mark Mitchell]

There is a key difference between the two questions - when the bonuses are awarded.

In 18.6, the bonus is awarded at the start of each year. So, whenever the person dies in the first year, they will have received one bonus, and the sum assured payable on death at any time in the first year is S*(1+b) (where S is the initial sum assured and b is the rate of bonus).

In Q18.10(iii)(c), the bonus is awarded continuously. So, assuming the person dies in the middle of the first year, they will have received half a year's bonus, and the sum assured paid on death half way through the first year is S*(1+b)^0.5. In your working, you are missing the power of 0.5 on the bonus in the first year (and later years similarly).