September 2016 Question 1 (ii)

[Tong_Tong]

Hello,

Could someone help with the explanation of the answer for question (ii)?

"If the interest rate charged to the policyholder is higher than the discount rate used to value the loan ...
... then a surplus results for each year the policy is in force ."

Why? As long as the interest rate charge is greater than the expense and below the value of the property then i thought it will generate a surplus regardless of the interest rate relative to the discount rate? Would it be possible to provide a numerical example?

Thanks,

 

[FT58]

I've just been doing the same paper - this is an example that might help:

Insurer lends policyholder £100,000 at the beginning of the year
Interest rate charged is 7% pa
Insurer uses a discount rate of 5% to value the loan

If the policyholder died right at the start of the year the insurer would receive £100,000 (assuming house could be sold immediately).

By the end of the year, the outstanding loan balance will be £107,000. So if the policyholder died after exactly one year the insurer would receive £107,000. This has a present value of 107,000/1.05 = c. £102,000

So I think the surplus is about £2,000 a year here.

 

[Tong_Tong]

I've just been doing the same paper - this is an example that might help:

Insurer lends policyholder £100,000 at the beginning of the year
Interest rate charged is 7% pa
Insurer uses a discount rate of 5% to value the loan

If the policyholder died right at the start of the year the insurer would receive £100,000 (assuming house could be sold immediately).

By the end of the year, the outstanding loan balance will be £107,000. So if the policyholder died after exactly one year the insurer would receive £107,000. This has a present value of 107,000/1.05 = c. £102,000

So I think the surplus is about £2,000 a year here.

Ah .... I understand.. thanks a bunch.