FOREACH variable vector

 Repeats the sequence of commands between the FOREACH command and the corresponding END command once for each element in the vector. Each time through the loop, variable takes on the value of successive elements from the second argument, vector. The vector may be a literal vector and it may have named constants as elements. So the following would be legal: ```NAME jan feb mar apr may jun \ jul aug sep oct nov dec FOREACH month jan,dec . . .'some computation using month END``` You can also use the two or three-term sequence notation to control the FOREACH loop as shown here: ```FOREACH n 1,10,0.1 LOG10 n log10N SCORE n Number SCORE log10N NaturalLog END PRINT table number naturalLog``` The above program segment will repeat the commands in the loop with n taking on the values from 1 through 10 in steps of 0.1. That is, the loop will be executed with n equal to 1, then to 1.1, then to 1.2, etc., until it reaches 10 (inclusive). The three terms of the sequence notation may also be variable names as shown here: ```FOREACH n low,high,step ... END``` And the sequence can be reversed to loop from high to low as shown here: ```FOREACH n low,high,step ... END``` The step value must always be positive. See also the BREAK, REPEAT, IF, UNTIL, and WHILE commands. This program shows the effect of the FOREACH command: ```COPY 1,10 Numbers FOREACH number numbers PRODUCT 1,number factorial SCORE factorial Factorials END PRINT table numbers factorials``` This produces: ```Numbers Factorials 1 1 2 2 3 6 4 24 5 120 6 720 7 5040 8 40320 9 362880 10 3.6288E06``` Here's a more practical application using the FOREACH command. It is a Monte Carlo simulation of investment performance: ```'Assume you are retiring and have 1 million dollars to 'invest and that you are considering investing it in a 'mutual fund that tracks the NASDAQ index. Assume further 'that each year you will withdraw \$80,000 from the fund for 'living expenses. 'Given the data for the historical annual changes in the NASDAQ 'index, analyze it to estimate the range of balances 'within 1 standard deviation of the mean if you invested 'as described. 'Also, calculate the probabilities of having a gain 'and a loss after 30 years as well as the probability of 'going broke sometime within the 30 years. Use variables 'for these numbers (1 million dollars, 30 years, \$80,000) so 'you can change the assumptions easily to compare scenarios. 'For simplicity, ignore costs, dividends, and inflation. 'Data from: ' http://www.finfacts.com/Private/curency/nasdaqcompositeperformance.htm 'Annual fractional price change of Nasdaq 1930--2006: DATA (0.1018 0.0173 -0.1733 0.0905 0.2214 \ 0.2390 0.3313 -0.1099 0.0553 -0.0924 0.0702 \ 0.2284 0.1045 0.0138 -0.0248 0.4553 0.1534 \ 0.1135 -0.1850 0.4155 0.0693 -0.0147 0.3166 \ -0.1502 0.2044 0.2312 0.1715 -0.0455 0.2659 \ 0.2577 -0.0236 -0.0984 0.2736 0.1718 -0.3106 \ -0.3511 0.2976 0.2610 0.0733 0.1231 0.2811 \ 0.3388 -0.0321 0.1867 0.1987 -0.1122 0.3115 \ 0.0753 -0.0526 0.1541 0.1926 -0.1780 0.5684 \ 0.1545 0.1475 -0.0320 0.3992 0.2271 0.2164 \ 0.3963 0.8559 -0.3929 -0.2105 -0.3153 0.5001 \ 0.0859 0.0137 -0.0188) nasdaqData DATA 30 numberOfYears DATA 1000000 initialInvestment DATA 80000 annualWithdrawal NAME 10000 repeatCount 'Add 1 to the gains to get annual gain factors ADD 1 nasdaqData nasdaqGainFactors REPEAT repeatCount COPY initialInvestment balance SAMPLE numberOfYears nasdaqGainFactors sampleHistory FOREACH yearlyGain sampleHistory MULTIPLY balance yearlyGain balance SUBTRACT balance annualWithdrawal balance IF balance <= 0 BREAK 'We're broke, so skip to next history END END SCORE balance FinalBalances END 'Compute median and 1 std dev below median and 1 above: PERCENTILE FinalBalances (15.87 50 84.13) oneStdevRangeOfBalances COUNT FinalBalances initialInvestment numberOfGainingPeriods COUNT FinalBalances <=0 numberOfBrokePeriods DIVIDE numberOfLosingPeriods repeatCount probabilityOfLoss DIVIDE numberOfGainingPeriods repeatCount probabilityOfGain DIVIDE numberOfBrokePeriods repeatCount probabilityOfGoingBroke PRINT " " initialInvestment numberOfYears annualWithdrawal PRINT probabilityOfGain probabilityOfLoss probabilityOfGoingBroke PRINT oneStdevRangeOfBalances%8.0F ```