Cafe II. If all the three Ages are between 15 and 55, and the Difference between the greatest and the least not more than 15, of the Sum of their Ages will be a mean Age. Example. Suppose three joint Lives on an Annuity of £200, A aged 26, B 32, and C 41. 26 32 41 3)99 33 7.1 200 £1420 Value required. Cafe III. If one or all the Ages are without the Limits if 15 and 55, multiply the Sum of the three correfponding Values by the Square of the leaft of them referving the Product, then multiply the two greater Values by each other, and to the Double of the Product add the Square of the leffer Value, which divide by the referved Product, and subtract the Quotient from twice the leffer Value, and the Remainder will give the Years Purchase. Example. Suppose three Ages are 12, 36, and 50, the Annuity £100, Intérest 4 per Cent. Solution. Prob. V. To find the Value of an Annuity upon the longest of three Lives. Cafe I. If the Ages are equal, the Answer will be. found at once by Table 5. Example. Suppofe three Ages, each 37 Years, on an Ane nuity of £150, Interest at 4 per Cent. Solution. 1 Solution. By Table 5. 37 = 17. 150 850 17 £2550 Value required. Cafe II. If none of the Ages are below 10 or above 60, and the Difference betwixt the greatest and leaft of them not exceeding 15, to double the Sum of the two laft, add the greateft, and take of the Sum for 45 a mean Age. Example. Suppose the Ages are 18, 28, and 32, Annuity £200, Intereft 4 per Cent. Solution. 18 x 2 = 36 28 x 2 = 56 32 5)124 24 19. 200 £ 3800 Value required. Cafe III. If the Ages do not correspond with the Limitations of the last Cafe, find the Value of the greatest of the given Ages by Table 3, and the Values correfponding to all the feveral Ages by Table 5, and let the Difference of the two Values anfwering to the greatest be taken and referved, let the Square of the greatest of these twa be divided by the Product of the two other remaining Values; multiply the Square of the Quotient by the referved Difference; then the laft Produft, added to the Value of the Annuity for the two youngest Lives, will give the Value to be required. Example. Suppose three Ages are 25, 35, and 50, Annuity £100, and Intereft 4 per Cent. B Y the foregoing Problems may be computed the Value of Annuities; and, by the following the Progreffion of Compound-Interest, as applicable to the Rate of Affurances, may be easily understood, being Problems for the Use of Tables 6, 7, 8, 9, and 10. Prob. I. Principal, Rate, and Time, being given, to find the Amount. Rule. Multiply the Amount of £1, in the first Table, at the Rate, and, for the Time given, by the propofed Principal, and the Product will give the Answer. Example. What will £500 amount to in 14 Years, Compound-Intereft at 4 per Cent? Solution. In Table 6, oppofite to 14 Years, and under 4 per Cent. you have 1.73167 500 £865.835 Answer. Prob. II. Principal, Rate, and Amount, being given, to find the Time. Rule. Divide the Amount by the Principal, and the Quotient will be the Amount of £1, at the given |