Math Problem Solver

A life insurance company issues a large number of 4-year unit-linked endowment assurance policies to

lives aged 65 exact. Level premiums are payable annually in advance until maturity or earlier death.

The company has performed a profit test on these policies and the profit vector per policy sold, ignoring

surrenders, is as follows:

(185.21, –121.52, –5.28, 12.95)

(i) Calculate the profit signature per policy sold if negative non-unit fund cash flows are zeroised. [3]

The company now wishes to allow for surrenders in its calculations. It assumes that at the end of the first

and second policy years only, 3% of the surviving policyholders will surrender. Surrender values are equal

to the bid value of units held (after deduction of the fund management charge) less a surrender penalty of

50.

(ii) Calculate the revised profit signature per policy sold after allowing for surrenders if negative non-unit

cash flows are zeroised. [6]

(iii) Calculate the net present value of the revised profit signature in part (ii), using a risk discount rate of

8% per annum. [1]

Basis:

Mortality AM92 Ultimate

Interest earned on non-unit cash flows 5% per annum fund

Expenses Ignore. [Total 10]