The Doctrine of Compound Interest: Illustrated and Applied to Perpetual Annuities, to Those for Terms of Years Certain, to Life-annuities, and Generally to Prospective Transactions, with New and Compendious Tables ...
subscribers, 1825 - 193 pages
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accomplished according accruing admitting already amongst amount annual Annuity for Ratio annum application ascertained average become calculation capital cent column comparative compound interest concerning consequence consideration considered continuance corresponding Cumulation Annuity debt Decrements deduced depending difference Discounted Annuity divided equal equations equivalent establish exhibit expectation expiration expressed follows forthcoming fraction further given Government half half-yearly instalments Improved Cumulated Principal income increase indicates individuals inquired invested joint latter less Life-annuities limited lives method Mortality multiplied observations obtained operation original payable payment period Perpetual persons population preceding present value probability produce progression proportion purchase quantity quarterly question RATIO of INTEREST Ratio of Principal reduced reference relative represented respective similar single solution solving specific subtracted successive sufficient supposed Table term terminable tion transactions unit unity Value of Annuity various whence whole yearly
Page 126 - Simpson, for finding the values of any three from the values given of any two joint lives. " Let A be the youngest, and C the oldest " of the three proposed lives. Take the " value of the two joint lives B and C, and " find the age of a single life D of the same " value. Then find the value of the joint " lives A and D, which will be the
Page 118 - This remainder multiplied by 23.574 (the value * When twice the expectation of the youngest life is greater than twice the expectation of the oldest life increased by unity and twice the perpetuity, the reserved quotient, instead of being subtracted from twice the perpetuity, must be added to it, and the sum, not the difference, multiplied by the perpetuity increased by unity.
Page 121 - A less the value of an Annuity on the longest of the two lives, B and C, combined with it.
Page 122 - Let a represent the number of persons living in the Table at the age of A, the younger of the two lives, a', a", a", &c. the decrements of life at the end of the 1st, 2d, 3d, &c. years from the age of A; b the number of persons living at the age of B, the older of the two lives, and c, d, e,f, &c. the number of persons living at the end of the 1st, 2d, 3d, &c. years from the age of B. Then will the value of S (the given sum), depending on the...
Page 116 - Let this value added to unity be divided by £ 1 in" creased by its interest for a Year. From the quotient " subtract the value of the life for the given term, and 41 the remainder being multiplied into the given sum will *
Page 122 - For if the probability of survivorship between any two persons be found, the probability between two persons one year younger is obtained with little difficulty ; and by proceeding in this manner a whole table may be speedily constructed.
Page 130 - England such as to afford local information equally authentic and extensive on the same subject, very little difference would be found to exist between the two progressions, expressive of the Decrements of human life for the one country and lor the otfyer.