REVERSION. 



Example 2. What is the present worth 

 of a perpetual annuity of 5(M. to com- 

 mence at the expiration of a lease of 

 which 5 years are unexpired? The value 

 of a perpetual annuity commencing 1 im- 

 mediately is, at 5 per cent, interest, 20 

 years purchase ; the value of an annuity 

 for 5 years is, by the Table, 4,329477 ; the 

 latter subtracted from the former, and 

 the remainder multiplied by 50, gives 

 783 -IDs. 6d. Ihe value of the reversion. 



Reversionary interests depending on a 

 life or lives, particularly when several 

 lives are concerned, form more intricate 

 questions ; but the cases which most com- 

 monly occur may be resolved by the fol- 

 lowing problems. 



Problem 1. A sum of money is to be 

 received at the death of a person, who is 

 now of a given age ; what is the value 

 thereof in present money ? 



Subtract the value of the life from the 

 perpetuity ; then, as the perpetuity is to 

 the remainder, so is the proposed sum to 

 its value in present money. 



Example. Let the'age be 30 years, and 

 the given sum 500/. Then the value of 

 the life being 13,072 and the perpetuity 

 20, it will be, as 20 : 6.928 : : 500/. : 173/. 

 4s. the value sought. 



Problem 2. To find the value of the 

 reversion of one life after another. 



From the value of the life in expecta- 

 tion subtract the value of the two joint 

 lives ; the remainder will be the requir- 

 ed value of the reversion. 



Example. Let the age of the life in 

 possession be 55 years, that of the life in 

 expectation 20 years, and the annuity 

 1001. Then, by Table V. (Article Awar ur- 

 n-its) the value of the two joint lives will 

 be 8,216, which subtracted from 14,007, 

 the value of the life in expectation, leaves 

 5,791 years purchase for the value of the 

 reversion ; which multiplied by the an- 

 nuity, gives 579/. 2s. its value in present 

 money. 



Problem 3. To find the value of the 

 reversion of two lives after one. 



From the value of the longest of the 

 three lives subtract the value of the life 

 in possession, the remainder will be the 

 value of the reversion. 



Example. Let the age of the life in 

 possession be 40 years, and the ages of 

 the two lives in expectation be 20 and 65 

 years; in this case, the value of the three 

 lives being 15,902, and that of the life in 

 possession 11,837, the answer will be 

 4,065 years purchase : so that, if the an- 

 nuity was to be 500/. the value of the re- 

 version would be 2032/. IQs. 



Problem 4. To find the value of an 

 annuity certain for a given term after the 

 extinction of any given life or lives. 



Subtract the value of the life or lives 

 from the perpetuity, and reserve the ic- 

 mainder: then say as the perpetuity, is to 

 the present value of the annuity certain, 

 so is the said reserved remainder to a 

 fourth proportional, which will be the 

 number of years purchase required. 



Example. Suppose A and his heirs 

 are entitled to an annuity certain for 14 

 years, to commence at the death of B, 

 aged 25. What is the present value of 

 A's interest in this annuity ? The value 

 of the life of B, is 13,567, which subtract- 

 ed from 20 (the perpetuity) leaves 6,433 

 for the remainder : therefore, as 20 is to 

 9,198, the value of an annuity certain for 

 14 years, so is 6,433 to 3,183, the number 

 of years purchase required. 



Problem 5. B, who is of a given age, 

 will, if he lives till the decease of A, whose 

 age is also given, become possessed of an 

 estate of a given value ; what is the 

 worth of his expectation in present mo- 

 ney ? 



Find the value of an annuity on two equal 

 joint lives, whose common age is equal to 

 the age of the oldest of the two proposed 

 lives, which value subtract from the per- 

 petuity, and take halt' the remainder; 

 then say, as the expectation of duration 

 of the younger of the t\\o lives is to that 

 of the older, so is the said half remainder 

 to a fourth proportional ; which will be 

 the number of years purchase required 

 when the life of B in expectation i the 

 older of the two ; but if B be the younger, 

 then add the value so found to that of the 

 joint lives A and B, and let the sum be 

 subtracted from the perpetuity, which 

 gives the answer in this case. 



Example 1. Suppose the age of A to 

 be 20, and that of B 30 years' ; and the 

 annual value of the estate 50/. Then the 

 value of two equal joint lives ,aged 30 

 being 10,255, and the perpetuity 20, the 

 difference will be 9,745, the halt of which 

 is 4,872. Therefore, as 33,43, the expecta- 

 tion of A, is to 28,27 the expectation, of B, 

 so is 4,872 to 4,119 years purchase, which 

 being multiplied by 50, the given annual 

 value, we have 205/. 19*. for the required 

 value of B's expectation. 



Example 2. Let the age of A be 30, 

 that of B 20 years ; and the rest as in the 

 preceding example. Then, the value of 

 the joint lives is 10,707, which being add- 

 ed to 4,119 found above, the sum is 14,826; 

 and this subtracted from 20,the perpetuity, 



