The questions are complete.

A single-premium policy provides the following benefits to a husband and wife each aged 40?

(1) An annuity of 5,000 per annum, payable continuously, commencing on the husband's

death within 25 years, or on his survival for 25 years, and continuing so long as either husband

or wife is alive.

(2) A return of half the single premium without interest immediately on the death of the

husband within 25 years, provided that his wife has already died.

The office issuing the contract uses the following basis:

mortality : A1967-70 ultimate

interest : 4% per annum

expenses are ignored.

Calculate the single premium.

A husband and wife, aged 70 and 64 respectively, effect a policy under which the benefits are

(1) a lump sum of 10,000 payable immediately on the first death, and (2) a reversionary

annuity of 5,000 p.a. payable continuously throughout the lifetime of the surviving spouse

after the death of the first. Level premiums are payable annually in advance until the first

death.

Calculate the annual premium on the undernoted basis:

Males' Mortality: a(55) males ultimate

Females' Mortality: a(55) females ultimate

Interest: 8% p.a.

Expenses: 10% of all premiums

on 3.? Verify the entries in Table 3.7.1 for De Moivre's law and Weibull's law. Consider a modication of De Moivre's law given by s(x)=(1) 05x 0. In this formula Mt} is the standard force of mortality. The symbol 3: denotes a vector of numerical information about the life at the time of selec- tion. This information would include the age and other classication infor- mation. It is required that Thur) :> 0 and 413:0) = 1, where x denotes standard information. Show that the select survival function is rpm = (ii-7m) and the p.d.f. of T(x), the random variable timemntil-death given the mfor- mation x, is 'I'{x) ,pfmlgphul)\""3"1, Where ,pfm] is the derivative with respect to t of arm]. This is called a proportional hazard model. 'PIExJ :cllcneous . A life at age 50 is subject to an extra hazard during the year of age 50 to 51. If the standard probability of death from age 50 to 51 is 0.006, and if the extra risk may be expressed by an addition to the standard force of mortality that decreases uniformly from 0.03 at the beginning of year to 0 at the end of the year, calculate the probability that the life will survive to age 51. . 1f the force of mortality ax\"), 0 5 t 5 1, changes to Mt) c where c is a positive constant, find the value of c for which the probability that (x) will die within a year will be halved. Express the answer in terms of em. . From a standard mortality table, a second table is prepared by doubling the force of mortality of the standard table. 15 the rate of mortality, qr; at any