3. _Rent-charges had a market-value, varying with time and place, and expressed as a number of years' purchase of the rent-charge._ The sellers of rent-charges were influenced by many motives: a lord wished to build a castle, or go on a crusade; a farmer wished to improve his estate; a merchant wished to embark on larger ventures. Opportunities thus opened in the cities for men of wealth to get a fixed income for a payment of ready money. In the cities, the buyers seeking a fixed income would bid down, or bid up, the value of the rent-charges, which thus came to have a quotable market value. In time, greater and greater amounts were paid by the investors in return for the guarantee of a given income. In rural districts the value of the charges was low, that is, the capital sum was but ten or twelve times the value of the annual rent-charge; while in the cities it rose to twenty and even twenty-five times the annual rent-charge. A memento of this practice, probably, is the manner in which the price paid for land is spoken of still in England and the continental countries in a phrase quite unfamiliar to American ears, as a certain number of "years' purchase." If an estate is sold for twenty times the annual net rental it is said to be sold at twenty "years' purchase." This does not mean that the rental for twenty years only is sold, but that the rental _in perpetuity_ is sold for twenty times the annual rent; that is, the land is sold outright for twenty years' rent paid at once. The estate is looked upon primarily as yielding a fixed income; the value of the permanent possession of the estate is thought of as a certain number of times the value of the income secured. "Years' purchase" means, therefore, the length of time required for the income to amount to the purchasing price. This attains the thought of the present value of the estate, or capital sum in it, though the capital sum is thought of as a multiple of the income, instead of the income being calculated as a percentage of the capital value. Now at the rate of "ten years' purchase" an investment of money in land affords an annual interest of ten per cent., as each year the rental is one tenth of the original investment; twelve years' purchase yields eight and one third per cent., twenty years' purchase, five per cent., and twenty-five years' purchase, four per cent. Increase in the number of years' purchase corresponds to a decrease in the rate of interest which the original investment of money, the capital sum, is expected to yield. This is equally true whether the investment be in the legal form of a purchase of the fee-simple of land, or in that of the purchase of a rent-charge. We are brought to this conclusion: that the present value of the rents in perpetuity, of any given wealth, is the capital value of the wealth; and that the reciprocal of the number of years' purchase is the rate of interest that an investment is expected to yield.