to “ The present value of a life annuity” is the sum that would be sufficient (allowing for the chance of life failing, which has been considered in the preceding pages) to pay the annuity without loss. If money bore no interest, the value of an annuity of 1l. would be equal to the expectation of life. Thus by the foregoing table, the value of an annuity for a life of 20 years of age, if money bore no interest, would be equal to nearly 33 years and a half purchase; that is, 331, 10s. in hand for each life, would be sufficient to pay any number of such lives 1l. per annum. If money is capable of being improved by being put out to interest, the sum just mentioned would be more than the value, because it would be more than sufficient to pay the annuity; and it will be as much more than sufficient as the interest is greater. As an example, If money can be improved at 5 per cent. compound interest, the half of 33l. 10s. or 161. 15s. will, in little more than 14 years, produce the 331. 10s. required. See Interest, Compound. It must not however be supposed, that 161. 15s. is the true value of an annuity of 1l. during a lite of 20. The value of an annuity certain for a term equal to the expectation, always exceeds the true value, because, in a number of life annuities, many of the payments would not be to be made till a much more remote period than the term equal to the expectation. Upon this principle the following table is computed, from which it appears that the present value of an annuity of 1l. on a life of 20 years age, is equal to 141. and a small fraction only ; that is, of 141. in hand for each life, improved at compound interest, will be sufficient to pay to any number of such lives 1l. per annum. TABLE I. Shewing the Value of an Annuity of 1l. on a Single Life, at every Age, according to the probabilities of the Duration of Human Life at Northampton, reckoning interest at 5 per cent. Ages. Valve, Age Value. ||Age Value. Age Value. Birth 8.863 1 year 11.563 2 13.420 3 14.135 4 | 14.613 5 14.827 6 15.041 7 15.166 8 15.226 9 15.210 10 15.139 11 15.043 12 14.937 13 14.326 14 14.710 15 14,588 16 14.460 17 14.334 18 14.217 39 14.108 20 14.007 21 13.917 22 13.853 23 13.746 24 13.658 25 13.567 50 10.269 | 75 4.744 TABLE II. Shewing the Value of an Annuity during the joint continuance of Two Lives, according to the probabilities of life at Northampton, reckoning interest at 5 per cent, beginning at the age of 10 and ending with that of 60. Ages.Value. ges.Value. | Ages.Value. | Ages. Value 10-10 12.665|15-75 4.49530-30 10.255 40-7015.298 10.15 12.30215-30 3.372|30-35 9.954 40-75/4.272 10-20 11.906|20-20 11.232 30-40 9.576 40-80 3.236 10-25 11.627 20-25 10.9891130-451 9.135 45-45 8.312 10-30 11.304|20-30 10.70730-50 8.596 45-507,891 10-35 10.916, 20-35 10.363 | 30-55 7.999 45-55 7,411 10-40 10.44220-40 9.937 30.60 7.292 45-60 6.822 10-45 9.900 120.45 9.448 30.65 6.447 45-65 6.094 10-50 9.260 20-50 8.861||30-70 5.442 45-705.195. 10.55 8.560 20 55 8.21630-75) 4.365 45-75 4.206 10-60 7.750 120-60 7.467 ||30-801 3.990 45-803.197 10-65 6.80320-65| 6.576||35-35 9.680 50-50 7.522 10-70 5.700 120-70 5.532|35-40 9.33150-55 7.098 10-75 4.522 120-75 4.42435-45 8.921 ||50-60/6.568 10 80 3.395 20-80 3.325|35-50 8.415 ||50-65|5.897 15-15 11.960 125-25 10.764 35-55 7.849 150-70 5.054 15-20 11.585 25-30 10.49935-60 7.174 50-75 4.112 15-25.11.324 25-35 10.175|35-65 6.36050-803,140 15.30 11.021 25-40| 9.771 35-701 5.382||55-55|6.739 15-35 10,655 125-45) 9.30135-75| 4.327 ||55-60 6.272 15 40,10,205 25-50 8.739 35-80) 3.268 55-65 5.671 15-45) 9.690 25-55 8.11640-40 9.016155-70/4.89$ 15-50 9.07625-60). 7.38340-45) 8.643|55-75 4.006 15-55 8.403 |25-65) 6.51540-50) 8.171 ||55-80 3.076 15-607 622 |25-70 5.439 40-55 7.654 60-60 5.888 15-65) 6.705 ||25-75 4.396|40-601 7.015 15-70) 5.631 H25-801-3.308 ||40-65) 6.2401 Application of the foregoing Tables. Table I. of any given age. RULE. " Multiply the number in the table against the given age, by the sum, and the product is the answer.” Ex. What should a person, aged 45, give to purchase an annuity of 60l. per annum during life, interest being reckoned 5 per cent. ? : The value in the table against 45 years is 11.105, and this multiplied by 60 gives the answer, 666l. 6s. Table II. To find the value of an anpuity on the longest of two single lives. Rule. " From the sum of the values of the single lives subtract the value of their joint continuance, and the remainder will give tbe value of the longest of the lives.” Ex. What is the value of the longest of two lives aged 10 and 15? 10 = 15.139 Table I. {The value of a life at 15 11.588 29.727 Table il. The value of the joint continu ance of two lives of 10 & 15 12.302 17.425 Therefore an annuity of 1001. a year upon the longest of two lives, one 10 and the other 15, 2 would be worth nearly 17 years and a half purchase, or more accurately, 17421. 108. Upon similar principles the value of the longest of three lives, &c. is found : and all other questions, relating to annuities, are likewise solved. See ReVERSIONS. Light, in physics, that substance, of the presence of which we are informed by the sensibility of the visual organs; from which bodies receive their colours; and which is, in some way, connected with heat. Light is an object of research, both in optics and in chemistry; the first inquires into its form and laws; the second, its essence. I. “Of light, in opties.'' Light, according to the Newtonian doctrine, which no subsequent discovery or theory seems to have discredited, is com, posed of inconceivably small particles of matter, of different magnitudes; which are emited or reflect- : ed from every point in the surface of a luminous body, in right lines, and in all directions, with an unparalleled velocity; and whose power or intensity decreases as the squares of the distance in crease. That light is a material substance, appears from its being propagated in time, and froin its acting upon and producing great alterations in other bodies; but that its particles are inconceivably small appears from this, that the greatest quantity of flame is foud to have scarce any sensible gravity or weight: also because these particles pervade the pores of all transparent bodies, however hard or heavy: yet, sınall as they are, the rays of light consist of different sorts of these particles; and that |
