A speculator on a Stock Market, aside from having money to spare, needs at least one other thing - a means of producing accurate and understandable predictions ahead of others in the Market, so that a tactical and price advantage can be gained. This work demonstrates that it is possible to predict one such Market to a high degree of accuracy. For the purpose, the Financial Times - Stock Exchange (F.T.-S.E.) 100 Share Index in the UK, known as 'The Footsie', was selected. Neural network predictions were obtained for the daily Market close 5 days ahead, and 25 days ahead, as measured in mean square error and in root mean square error. To measure percentage accuracy, each individual test case prediction was compared with the actual market outcome, and total percentage accuracy for the whole test set was similarly calculated. Comparisons were also drawn with predictions for the same test cases using four types of Multiple Linear Regression. The neural network results indicated that predictions based upon the lowest mean square error bear little relationship to the same test cases, when measured in terms of overall percentage accuracy. For the lay person, or a Stock-Market speculator, it was also shown that predictions can be produced to a high level of accuracy, in a readily understandable format.