REVERSION, a sum of money, estate, annuity, or any other kind of property, the possession of which is not to be ob tained till after the expiration of a certain period of time, or till some event, as the failure of a life or lives, has happened. The present value of such property de pends greatly on the current interest of money, for if money produced only three per cent. interest, a person giving 10001. for a reversionary estate relinquishes an annuity of 301., but if he could make five per cent. interest of his money, he gives up an annuity of 50/. and consequently in the latter case he would exifect a greater reversion than the former. The true va lue of a reversion therefore is that present sum, which if improved at a given rate of interest, would at the period when the reversion comes into possession amount to its then actual value. This, with res pect to sums receivable at the end of a certain number of years, is easily found by Table II. article INTEREST, Thus, if a person is entitled to 5001. at the end of ten years, and wishes to know its present worth : the value of one pound to be received at the end of this term is, by the Table, 613913, which mul tiplied by 500 gives 3061. 19s. ld. for the present value of the reversion. In a simi lar manner the present worth of the re version of an annuity or estate after a cer tain number of years may be found by Table IL article ANNUITIES.
Example 1. What is the present value of an annuity of 211. for the term of 30 years, but which is not to commence till the expiration of 7 years from the pre sent time ? The present value of an an nuity of one pound for 30 years is, by the Table, 15,372451, which multiplied by 21 gives 322,8214; but as each pay ment of the annuity is to be received 7 years later than if it •commenced immedi ately, this sum must be multiplied by the value of one pound to be received at the end of 7 years, or, .710681, which gives 2291. 8s. 5d. for the present worth of the, reversion.
Example 2. What is the present worth of a perpetual annuity of 50/. to com mence at the expiration of a lease of which 5 years are unexpired ? The value of a perpetual annuity commencing 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 7831.40s. 6d. the 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 5001. Then the value of the life being 13,072 and the perpetuity 20, it will be, as 20 : 6.928 : : 500l.: 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 100/. Then, by Table V. (Article 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 5791. 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.