Volume 1

Observations on reversionary payments; on schemes for providing annuities for widows, and for persons in old age; on the method of calculating the values of assurances on lives; and on the national debt. Also, essays on different subjects in the doctrine of life-annuities and political arithmetic ... / by Richard Price. The whole new arranged, and enlarged ... by William Morgan.

  • Price, Richard, 1723-1791.
Date:
1812
Catalogue details

Licence: Public Domain Mark

Credit: Observations on reversionary payments; on schemes for providing annuities for widows, and for persons in old age; on the method of calculating the values of assurances on lives; and on the national debt. Also, essays on different subjects in the doctrine of life-annuities and political arithmetic ... / by Richard Price. The whole new arranged, and enlarged ... by William Morgan. Source: Wellcome Collection.

    403/474 (page 349)
    ment, at the end of the gtb year, may be found RO wee ue Ma FO OS to be ne | Se Tie | x | a ay? Or | es x “ and the present value. of all the possible payments, 1 a —8 1 n—9 Oy 2 BO 3 mes en a ~ 073 x Fr Bice : 3 ae iy J n—7 mm 7 But this series is equal to = X ——- X Ss x 8 n m a—& 1 n—Q 2 n-= 10 3 =a dees a = ae Sere Aer n— 77 m— 7 n—7r m— 7 nan—7r m—7 nee n—§ 1 n—9 &e, Nows=e X ——— f= = X —-)» &e. n— Tr m—7 n—7r* grat Fier es! is the value of an annuity for a life seven years older than the expectant, after another life seven years older than the life whose complement iS 7. a= y™=7 is the probability that both the rt m assigned lives shall continue 7 years. And 5 is the value of 1 due at the end of 7 years. ‘The rule, therefore, given for solving this question, 1s right. This demonstration, as well as that in the last note, is, for the sake of more ease and clearness, applied to the hypothesis of an equal decrement of life. It does not, however, depend upon it, but may be applied to any table of observations (y). (vy) Leta, &, c, d, e, f, &c., represent the same quantities as in the preceding Note. Let m represent the number of persons living at the age of B, and ”, 0, D, J % &c. the number living at the end of the Ist, ad, 3d, &c. years from the age-of B.—By reasoning in the same manner with Dr. Price in the solution of this question, and supposing the first payment of the annuity to become due at the end of the 4th year, its present value will be = =i Pai = i a mr amr3 _ Pe —<-~ the present value of the payment at the end | of