(Table VII.) and likewise by the probability that the life will continue so long (Prob. II.) Subtract the product from the present value of the given life (Table III.), and the remainder multiplied by the annuity will give the answer. Examples. (1.) What is the value of an annuity of £100 for 14 years, provided a person aged 35 lives so long? Interest 5 per cent. The value of a life of 35+14=49 (Table III.) is The value of a life of 35 (Table III.) is 10.443 •5050679 12.502 The probability that a life of 35 will continue 14 years (by Table I. (2.) What is the value of an annuity of £80 for 20 years, provided a person aged 45 lives so long? Interest at 5 per cent. PROBLEM XIV. To find the present value of an annuity certain for a given term, after the extinction of any given life or lives. RULE. Multiply the value of an annuity on the given life or lives by the interest of £1 for a year, subtract the product from an unit, and reserve the remainder. Find the present worth of an annuity certain for the given term, (page 252) which multiply by the reserved remainder already found, and the product will be the value required. Examples. (1.) A person A, or his heirs, are entitled to an an. nuity for 21 years, to commence at the death of a gen gentleman aged 70, what is the present value of A.'s interest in the annuity, interest at 5 per cent.? The value of an annuity on a life of 70 (Table III.) is 6·023, which multiplied by 05, and deducted from an unit leaves 69885, the reserved remainder. The present worth of £1 annuity certain for 21 years (page 252) is 12-82115; then 12-82115×·69885=8′96 years' purchase, the value of A.'s interest. (2.) A lease of an estate is held upon two lives, aged 60 and 70, and after the decease of both, for 21 years certain; what is the value of the lease, reckoning interest at 5 per cent.? (3.) A lease of an estate is held upon three lives aged 50, 60, and 70, and after their decease, for 21 years certain; what is the value of the lease, interest at 5 per cent.? PROBLEM XV. To find the present value of an estate, to be entered upon at the extinction of any given life or lives. * RULE. Find the value of an annuity of £1, to continue for ever (by prop. 1, page 259), and the value of an annuity on the given life or lives (Table III. or V.) The difference between these two values will be the answer required. Examples. (1.) What is the value of a freehold estate to be entered upon at the death of a person aged 20, interest at 5 per cent.? First 105 £20, the value of the perpetuity, and the value of a life of 20, (Table III.) is 14-007, hence 20-14.007-5.993, the value required; so that the estate is worth about 6 years' purchase. (2.) What is the value of a freehold estate, to be entered upon at the death of either of two persons, aged 40 and 45, interest at 5 per cent. ? (3.) What would be the value of a freehold estate, to Or for a given number of years by Theorem I, page 252. be entered upon at the death of both the persons mentioned in the preceding example, interest at 5 per cent.? (4.) A person aged 70 has the lease of a house for 80 years, at a ground rent of £10 per annum, which he lets for £60 a year, what must the present tenant pay down that he may hold the lease after the death of the proprietor, or what additional rent must he pay for the same advantage? TABLE I. Shewing the Probabilities of the Duration of Human Life, according to the Observations made at Northampton. Age Living. Dying. Age. Living. Dying. Age. Living. Dying. N. B. Of 11650 infants born, 3000 will die in the first year. Of the 8650 who live to be one year old, 1367 will die in the course of the second year, &c. TABLE II. Shewing the Expectations of Human Life at every Age, deduced from the Observations made at Northampton. Age. Expectation. Age. Expectation. Age. Expectation. Age. Expectation.| N. B. By expectation of life, must be understood, that out of a number of persons living, of a given age, one with another may expect to live a certain number of years, some of them enjoying a duration as much longer as others fall short of that period. A person of 45 years of age, may live 20.52 years; of 60 years of age, 13.21 years, &c. Females, in general, live longer than males, and married women live longer than single women, |