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  • Net present value

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    In finance, the net present value (NPV) or net present worth (NPW) is the summation of the present (now) value of a series of present and future cash flows. Because NPV accounts for the time value of money NPV provides a method for evaluating and comparing products with cash flows spread over many years, as in loans, investments, payouts from insurance contracts plus many other applications. Time value of money dictates that time affects the value of cash flows. For example, a lender may offer 99 cents for the promise of receiving $1.00 a month from now, but the promise to receive that same dollar 20 years in the future would be worth much less today to that same person (lender), even if the payback in both cases was equally certain. This decrease in the current value of future cash flows is based on a chosen rate of return (or discount rate). If for example there exists a time series of identical cash flows, the cash flow in the present is the most valuable, with each future cash flow becoming less valuable than the previous cash flow.

  • Kin selection

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    The co-operative behaviour of social insects like the honey bee can be explained by kin selection.Kin selection is the evolutionary strategy that favours the reproductive success of an organism's relatives, even at a cost to the organism's own survival and reproduction. Kin altruism can look like altruistic behaviour whose evolution is driven by kin selection. Kin selection is an instance of inclusive fitness, which combines the number of offspring produced with the number an individual can ensure the production of by supporting others, such as siblings. Charles Darwin discussed the concept of kin selection in his 1859 book, The Origin of Species, where he reflected on the puzzle of sterile social insects, such as honey bees, which leave reproduction to their mothers, arguing that a selection benefit to related organisms (the same "stock") would allow the evolution of a trait that confers the benefit but destroys an individual at the same time. R.A. Fisher in 1930 and J.B.S. Haldane in 1932 set out the mathematics of kin selection, with Haldane famously joking that he would willingly die for two brothers or eight cousins. In 1964, W.D. Hamilton popularised the concept and the major advance in the mathematical treatment of the phenomenon by George R. Price which has become known as Hamilton's rule. In the same year John Maynard Smith used the actual term kin selection for the first time. According to Hamilton's rule, kin selection causes genes to increase in frequency when the genetic relatedness of a recipient to an actor multiplied by the benefit to the recipient is greater than the reproductive cost to the actor. Hamilton proposed two mechanisms for kin selection. First, kin recognition allows individuals to be able to identify their relatives. Second, in viscous populations, populations in which the movement of organisms from their place of birth is relatively slow, local interactions tend to be among relatives by default. The viscous population mechanism makes kin selection and social cooperation possible in the absence of kin recognition. In this case, nurture kinship, the treatment of individuals as kin as a result of living together, is sufficient for kin selection, given reasonable assumptions about population dispersal rates. Note that kin selection is not the same thing as group selection, where natural selection is believed to act on the group as a whole. In humans, altruism is both more likely and on a larger scale with kin than with unrelated individuals; for example, humans give presents according to how closely related they are to the recipient. In other species, vervet monkeys use allomothering, where related females such as older sisters or grandmothers often care for young, according to their relatedness. The social shrimp Synalpheus regalis protects juveniles within highly related colonies.

  • Premium Bond

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    An ERNIE money box. A Premium Bond is a lottery bond issued by the United Kingdom government's National Savings and Investments agency. The bonds are entered in a regular prize draw and the government promises to buy them back, on request, for their original price. The bonds were introduced by Harold Macmillan in 1956. The government pays interest on the bond (1.40% per year as at December 2017). Interest is paid into a fund from which a monthly lottery distributes tax-free prizes to bondholders whose numbers are selected randomly. The machine that generates numbers is ERNIE, for Electronic Random Number Indicator Equipment. Prizes range from £25 to £1,000,000. Between 2005 and 2009, there were two £1m prizes each month and the minimum prize was £50, but prizes were reduced after the 2009 drop in interest rates. A second £1m prize was reintroduced in August 2014. Investors can buy bonds at any time which have to be held for a calendar month before they qualify for a prize. Numbers are entered in the draw each month, with an equal chance of winning, until the bond is cashed. Winners of the jackpot are told on the first working day of the month, although the actual date of the draw varies. The online prize finder is updated by the third or fourth working day of the month. From 1 January 2009 the odds of winning a prize for each £1 of bond was 36,000 to 1. In October 2009, the odds returned to 24,000 to 1 with the prize fund interest rate increase. The odds reached 26,000 to 1 by October 2013 and then reverted to 24,500 to 1 in November 2017. As of July 2018, each person may own bonds up to £50,000. Bonds can be bought in units of £1 after the first £100, with a value of £1 per bond and a minimum purchase of 100 bonds (or 50 bonds when paying by standing order). When introduced in 1957 they were popular – the only other similar game was football pools. The National Lottery did not exist until 1994. In Ireland, the Prize Bond originated in early 1957.

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