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Published online by Cambridge University Press: 18 August 2016
The late Mr. William Morgan, in the second edition of his Principles and Doctrine of Assurances and Annuities on Lives, published in the year 1821, has, in the 7th Problem of that work, investigated “the method of determining the amount of an annuity forborn and improved at compound interest during the continuance of a given life.” This problem he has subsequently discussed in an algebraical form, in Note V., page 154; and he has moreover given a table (Table VII.) showing the sum to which an annuity for-born and improved at 4 per cent, compound interest will amount, on the extinction of a given life, computed according to the foregoing method, from the Northampton Table of Observations.
page 2 note * This is not quite clearly expressed: instead of the word “accumulation” merely being employed, Mr. Morgan should have said, ‘the accumulation on the first payment at the end of the first year, and on the second payment,’ &c., &c.; its meaning is, however, sufficiently obvious.
page 4 note * See a paper on this subject in the Assurance Magazine, vol. i.
page 5 note * See Twelfth Report of Registrar-General, Table XV., page 10 in Appendix.
page 7 note * See Assurance Magazine, vol. ii., page 259.
page 7 note † This may be thus shown :
