CM1 - Practice Question 19.5

[Joi]

Good day.

Can someone explain me on CM1 Practice Question 19.5 Solution (right hand side), why 1.005*10000* D65/D[35] * a(12) 65 ?
I get the first 2 and last 2 values correctly but I am confuse if the middle part {1.005*10000* D65/D[35] * a(12) 65} is combination of {age 65 the life receives a whole life annuity of £10,000 pa payable monthly in arrears. and claims: 0.5% of each annuity payment} ?

My answer is:
{age 65 the life receives a whole life annuity of £10,000 pa payable monthly in arrears.} = 10,000a(12)65
plus
{claims: 0.5% of each annuity payment} =0.005PA[35]:30

Hence my answer for the middle part is 10,000a(12)65 + 0.005PA[35]:30 instead of 1.005*10000* D65/D[35] * a(12) 65

Thank you.

 

[Tushar Gora]

Hi Joi,

The annuity benefit starts at the age of 65, but we have to calculate the EPV for age 35.

10,000a(12)65 part of your answer calculates the EPV of annuity to age 65 only and not till age 35.

So, 10,000a(12)65 needs to be discounted further till age 35.
We do this by multiplying the part by: v^30 * 30p[35].

Now, v^30 * 30p[35] = PA[35]:30 = D65/D[35]

Plus, 0.5% of each annuity payment means 0.5% of 10,000a(12)65 will be included as a claim cost. Same as before you have to discount this value back to age 35.

Elaborate calculation;

At age 65, EPV = 10,000a(12)65 + 0.005*10,000a(12)65
= 10,000a(12)65 (1+0.005)

Discounting till age 35,
EPV = v^30 * 30p[35] * { 10,000a(12)65 (1+0.005) }
= D65/D[35] * { 10,000a(12)65 (1+0.005) }

Hope this helps!

 

[Joi]

Hi Joi,

The annuity benefit starts at the age of 65, but we have to calculate the EPV for age 35.

10,000a(12)65 part of your answer calculates the EPV of annuity to age 65 only and not till age 35.

So, 10,000a(12)65 needs to be discounted further till age 35.
We do this by multiplying the part by: v^30 * 30p[35].

Now, v^30 * 30p[35] = PA[35]:30 = D65/D[35]

Plus, 0.5% of each annuity payment means 0.5% of 10,000a(12)65 will be included as a claim cost. Same as before you have to discount this value back to age 35.

Elaborate calculation;

At age 65, EPV = 10,000a(12)65 + 0.005*10,000a(12)65
= 10,000a(12)65 (1+0.005)

Discounting till age 35,
EPV = v^30 * 30p[35] * { 10,000a(12)65 (1+0.005) }
= D65/D[35] * { 10,000a(12)65 (1+0.005) }

Hope this helps!

Thank you so much!!