Discrete Annual Compound InterestInterest Rate

20.00%

Year Cash Balance0 $1,000.001 $1,200.002 $1,440.003 $1,728.004 $2,073.605 $2,488.326 $2,985.987 $3,583.188 $4,299.829 $5,159.78

10 $6,191.74

Oxford University Press (2011) pp. 683-693Note: This discrete annual compound interest example is from Simon Benninga, Principles of Finance with Excel, Second Edition

Column B

Principles of Finance with Excel, Second Edition

Column B

Excel uses standard "PEMDAS" order of operations for arithmetic "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction"

Parentheses "(6-3)" Exponents - use caret "^" (for example, "six squared" is "6^2"; Multiplication - use asterisk "*" "square root of six" is "6^(.5)")Division - use slash "/"Addition "+"Subtraction "-"

Assume we want (6-3)(4+2) = 1818

Assume we want (3/5) squared0.36

Excel uses standard "PEMDAS" order of operations for arithmetic "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction"

(for example, "six squared" is "6^2"; "square root of six" is "6^(.5)")

Example note - general practice throughout the course is to round answers to two decimal placesnatural log function log to the base "e" of 1.5 1.5"ln" 0.41 0.41

log to the base 2 log to the base 2 of 1.5"log(number, base)" 0.58

pi function 1 divided by the square root of pi"pi()" 0.56

random number between 0 and 1"=rand()" 0.97

0.920.41

A B C D E1234567891011121314

note - general practice throughout the course is to round answers to two decimal placesF G H I

1234567891011121314

Adjusted monthly closing prices (from Yahoo Finance)

Date S&P 500 Index Duke Energy Stock8/1/14 1925.15 72.94

7/1/2014 1930.67 72.136/2/2014 1960.23 74.19

5/1/14 1923.57 71.084/1/2014 1883.95 73.683/3/2014 1872.34 70.452/3/2014 1859.45 70.111/2/2014 1782.59 69.09

12/2/2013 1848.36 67.5111/1/2013 1805.81 68.4410/1/2013 1756.54 69.419/3/2013 1681.55 64.628/1/2013 1632.97 63.487/1/2013 1685.73 67.956/3/2013 1606.28 64.65/1/2013 1630.74 64.054/1/2013 1597.57 71.23/1/2013 1569.19 68.732/1/2013 1514.68 65.571/2/2013 1498.11 64.37

12/3/2012 1426.19 59.7411/1/2012 1416.18 59.7610/1/2012 1412.16 60.769/4/2012 1440.67 59.928/1/2012 1406.58 59.917/2/2012 1379.32 61.986/1/2012 1362.16 63.265/1/2012 1310.33 60.34/2/2012 1397.91 58.113/1/2012 1408.47 56.982/1/2012 1365.68 56.731/3/2012 1312.41 57.12

12/1/2011 1257.6 58.9711/1/2011 1246.96 55.8810/3/2011 1253.3 54.079/1/2011 1131.42 52.938/1/2011 1218.89 50.077/1/2011 1292.28 48.566/1/2011 1320.64 49.165/2/2011 1345.2 48.95

4/1/2011 1363.61 48.083/1/2011 1325.83 46.792/1/2011 1327.22 46.381/3/2011 1286.12 45.47

12/1/2010 1257.64 45.2911/1/2010 1180.55 44.6310/1/2010 1183.26 45.79/1/2010 1141.2 44.448/2/2010 1049.33 43.117/1/2010 1101.6 42.326/1/2010 1030.71 39.595/3/2010 1089.41 39.494/1/2010 1186.69 40.943/1/2010 1169.43 39.812/1/2010 1104.49 39.891/4/2010 1073.87 39.74

12/1/2009 1115.1 41.3811/2/2009 1095.63 40.110/1/2009 1036.19 37.479/1/2009 1057.08 37.298/3/2009 1020.62 36.697/1/2009 987.48 36.116/1/2009 919.32 34.035/1/2009 919.14 334/1/2009 872.81 31.683/2/2009 797.87 32.852/2/2009 735.09 30.91/2/2009 825.88 34.23

12/1/2008 903.25 33.9111/3/2008 896.24 35.1610/1/2008 968.75 36.479/2/2008 1166.36 38.818/1/2008 1282.83 38.837/1/2008 1267.38 38.646/2/2008 1280 38.25/1/2008 1400.38 40.624/1/2008 1385.59 39.783/3/2008 1322.7 38.782/1/2008 1330.63 38.11/2/2008 1378.55 40.04

12/3/2007 1468.36 43.311/1/2007 1481.14 42.4910/1/2007 1549.38 40.69

9/4/2007 1526.75 39.678/1/2007 1473.99 38.937/2/2007 1455.27 35.726/1/2007 1503.35 38.395/1/2007 1530.62 40.994/2/2007 1482.37 42.63/1/2007 1420.86 42.132/1/2007 1406.82 40.861/3/2007 1438.24 40.46

12/1/2006 1418.3 39.6611/1/2006 1400.63 37.8810/2/2006 1377.94 37.49/1/2006 1335.85 35.78/1/2006 1303.82 35.467/3/2006 1276.66 35.466/1/2006 1270.2 34.355/1/2006 1270.09 33.014/3/2006 1310.61 33.693/1/2006 1294.87 33.732/1/2006 1280.66 32.861/3/2006 1280.08 32.44

12/1/2005 1248.29 31.4111/1/2005 1249.48 30.7410/3/2005 1207.01 29.949/1/2005 1228.81 32.998/1/2005 1220.33 32.787/1/2005 1234.18 33.46/1/2005 1191.33 33.625/2/2005 1191.5 31.084/1/2005 1156.85 32.683/1/2005 1180.59 31.362/1/2005 1203.6 30.221/3/2005 1181.27 29.69

12/1/2004 1211.92 28.0811/1/2004 1173.82 28.0210/1/2004 1130.2 26.99/1/2004 1114.58 25.18/2/2004 1104.24 24.287/1/2004 1101.72 23.286/1/2004 1140.84 21.975/3/2004 1120.68 21.594/1/2004 1107.3 22.493/1/2004 1126.21 24.13

2/2/2004 1144.94 23.451/2/2004 1131.13 22.91

12/1/2003 1111.92 21.5611/3/2003 1058.2 19.0210/1/2003 1050.71 18.849/2/2003 995.97 18.498/1/2003 1008.01 17.737/1/2003 990.31 17.936/2/2003 974.5 20.395/1/2003 963.59 19.84/1/2003 916.92 17.683/3/2003 848.18 14.622/3/2003 841.15 13.581/2/2003 855.7 16.81

12/2/2002 879.82 19.2911/1/2002 936.31 19.4910/1/2002 885.76 19.939/3/2002 815.28 19.028/1/2002 916.07 26.17/1/2002 911.62 24.546/3/2002 989.82 29.945/1/2002 1067.14 30.824/1/2002 1076.92 36.633/1/2002 1147.39 36.122/1/2002 1106.73 33.731/2/2002 1130.2 33.06

12/3/2001 1148.08 37.2211/1/2001 1139.45 34.2710/1/2001 1059.78 36.169/4/2001 1040.94 35.648/1/2001 1133.58 37.017/2/2001 1211.23 36.096/1/2001 1224.38 36.465/1/2001 1255.82 42.734/2/2001 1249.46 43.433/1/2001 1160.33 39.72/1/2001 1239.94 37.851/2/2001 1366.01 33.74

12/1/2000 1320.28 39.3311/1/2000 1314.95 41.4910/2/2000 1429.4 39.629/1/2000 1436.51 39.318/1/2000 1517.68 34.29

7/3/2000 1430.83 28.056/1/2000 1454.6 25.635/1/2000 1420.6 26.494/3/2000 1452.43 25.93/1/2000 1498.58 23.652/1/2000 1366.42 21.851/3/2000 1394.46 25.75

Monthly continuously compounded (log) returns

S&P 500 Index Duke Energy Stock -0.29% 1.12%-1.52% -2.82%1.89% 4.28%2.08% -3.59%0.62% 4.48%0.69% 0.48%4.22% 1.47%

-3.62% 2.31%2.33% -1.37%2.77% -1.41%4.36% 7.15%2.93% 1.78%

-3.18% -6.80%4.83% 5.06%

-1.51% 0.86%2.06% -10.58%1.79% 3.53%3.54% 4.71%1.10% 1.85%4.92% 7.46%0.70% -0.03%0.28% -1.66%

-2.00% 1.39%2.39% 0.02%1.96% -3.40%1.25% -2.04%3.88% 4.79%

-6.47% 3.70%-0.75% 1.96%3.09% 0.44%3.98% -0.69%4.27% -3.19%0.85% 5.38%

-0.51% 3.29%10.23% 2.13%-7.45% 5.55%-5.85% 3.06%-2.17% -1.23%-1.84% 0.43%-1.36% 1.79%

2.81% 2.72%-0.10% 0.88%3.15% 1.98%2.24% 0.40%6.33% 1.47%

-0.23% -2.37%3.62% 2.80%8.39% 3.04%

-4.86% 1.85%6.65% 6.67%

-5.54% 0.25%-8.55% -3.61%1.47% 2.80%5.71% -0.20%2.81% 0.38%

-3.77% -4.04%1.76% 3.14%5.58% 6.78%

-2.00% 0.48%3.51% 1.62%3.30% 1.59%7.15% 5.93%0.02% 3.07%5.17% 4.08%8.98% -3.63%8.20% 6.12%

-11.65% -10.23%-8.95% 0.94%0.78% -3.62%

-7.78% -3.66%-18.56% -6.22%-9.52% -0.05%1.21% 0.49%

-0.99% 1.15%-8.99% -6.14%1.06% 2.09%4.65% 2.55%

-0.60% 1.77%-3.54% -4.97%-6.31% -7.83%-0.87% 1.89%-4.50% 4.33%1.47% 2.54%

3.52% 1.88%1.28% 8.61%

-3.25% -7.21%-1.80% -6.55%3.20% -3.85%4.24% 1.11%0.99% 3.06%

-2.21% 0.98%1.40% 2.00%1.25% 4.59%1.63% 1.28%3.10% 4.65%2.43% 0.67%2.11% 0.00%0.51% 3.18%0.01% 3.98%

-3.14% -2.04%1.21% -0.12%1.10% 2.61%0.05% 1.29%2.51% 3.23%

-0.10% 2.16%3.46% 2.64%

-1.79% -9.70%0.69% 0.64%

-1.13% -1.87%3.53% -0.66%

-0.01% 7.86%2.95% -5.02%

-2.03% 4.12%-1.93% 3.70%1.87% 1.77%

-2.56% 5.58%3.19% 0.21%3.79% 4.08%1.39% 6.93%0.93% 3.32%0.23% 4.21%

-3.49% 5.79%1.78% 1.74%1.20% -4.08%

-1.69% -7.04%-1.65% 2.86%

1.21% 2.33%1.71% 6.07%4.95% 12.53%0.71% 0.95%5.35% 1.88%

-1.20% 4.20%1.77% -1.12%1.61% -12.86%1.13% 2.94%4.96% 11.32%7.79% 19.00%0.83% 7.38%

-1.71% -21.34%-2.78% -13.76%-6.22% -1.03%5.55% -2.23%8.29% 4.67%

-11.66% -31.64%0.49% 6.16%

-8.23% -19.89%-7.52% -2.90%-0.91% -17.27%-6.34% 1.40%3.61% 6.85%

-2.10% 2.01%-1.57% -11.85%0.75% 8.26%7.25% -5.37%1.79% 1.45%

-8.53% -3.77%-6.63% 2.52%-1.08% -1.02%-2.54% -15.87%0.51% -1.62%7.40% 8.98%

-6.64% 4.77%-9.68% 11.49%3.41% -15.33%0.40% -5.35%

-8.35% 4.61%-0.50% 0.79%-5.50% 13.66%5.89% 20.09%

-1.65% 9.02%2.37% -3.30%

-2.22% 2.25%-3.13% 9.09%9.23% 7.92%

-2.03% -16.42%#DIV/0! #DIV/0!

176 months - 175 returnsreturn data located rows 4 - 178Functions on one column at a timeS&P 500 Index Duke Energy Stock average monthly return

0.18% 0.59%average annual return

2.21% 7.14%standard deviation of monthly returns

4.47% 6.52%annualized standard deviation of returns

15.50% 22.60%minimum

-18.56% -31.64%maximum

10.23% 20.09%

Functions on two columns at the same time (ordered pairs) S&P 500 Index - x axis Duke Energy Stock - y axisDescription of best-fit (regression) line - Duke on S&P 500slope 0.49

y-intercept 0.0051

correlation 0.33

R-squared 0.111

-25.00% -20.00% -15.00% -10.00% -5.00% 0.00% 5.00% 10.00% 15.00%

f(x) = 0.4862708207x + 0.0050536106R = 0.1112460823 Column E

Linear (Column E)Linear (Column E)

-25.00% -20.00% -15.00% -10.00% -5.00% 0.00% 5.00% 10.00% 15.00%

f(x) = 0.4862708207x + 0.0050536106R = 0.1112460823 Column E

Linear (Column E)Linear (Column E)

-25.00% -20.00% -15.00% -10.00% -5.00% 0.00% 5.00% 10.00% 15.00%

f(x) = 0.4862708207x + 0.0050536106R = 0.1112460823 Column E

Linear (Column E)Linear (Column E)

Date S&P 500 Index Duke Energy Stock ### 10.23% 2.13%

3/1/2000 9.23% 7.92%4/1/2009 8.98% -3.63%9/1/2010 8.39% 3.04%

### 8.29% 4.67%3/2/2009 8.20% 6.12%4/1/2003 7.79% 19.00%4/2/2001 7.40% 8.98%

### 7.25% -5.37%7/1/2009 7.15% 5.93%7/1/2010 6.65% 6.67%

### 6.33% 1.47%8/1/2000 5.89% 20.09%3/1/2010 5.71% -0.20%

### 5.58% 6.78%### 5.55% -2.23%### 5.35% 1.88%

5/1/2009 5.17% 4.08%5/1/2003 4.96% 11.32%

### 4.95% 12.53%1/2/2013 4.92% 7.46%7/1/2013 4.83% 5.06%4/1/2008 4.65% 2.55%

### 4.36% 7.15%1/3/2012 4.27% -3.19%4/2/2007 4.24% 1.11%2/3/2014 4.22% 1.47%2/1/2012 3.98% -0.69%6/1/2012 3.88% 4.79%

### 3.79% 4.08%### 3.62% 2.80%

3/1/2002 3.61% 6.85%3/1/2013 3.54% 4.71%7/1/2005 3.53% -0.66%9/4/2007 3.52% 1.88%9/1/2009 3.51% 1.62%

### 3.46% 2.64%1/2/2001 3.41% -15.33%8/3/2009 3.30% 1.59%5/1/2007 3.20% -3.85%

### 3.19% 0.21%2/1/2011 3.15% 1.98%

### 3.10% 4.65%3/1/2012 3.09% 0.44%5/2/2005 2.95% -5.02%9/3/2013 2.93% 1.78%2/1/2010 2.81% 0.38%4/1/2011 2.81% 2.72%

### 2.77% -1.41%1/3/2006 2.51% 3.23%9/1/2006 2.43% 0.67%9/4/2012 2.39% 0.02%6/1/2000 2.37% -3.30%

### 2.33% -1.37%1/3/2011 2.24% 0.40%8/1/2006 2.11% 0.00%

5/1/14 2.08% -3.59%5/1/2013 2.06% -10.58%8/1/2012 1.96% -3.40%6/2/2014 1.89% 4.28%2/1/2005 1.87% 1.77%

### 1.79% 1.45%4/1/2013 1.79% 3.53%

6/1/2004 1.78% 1.74%8/1/2003 1.77% -1.12%

### 1.76% 3.14%1/2/2004 1.71% 6.07%

### 1.63% 1.28%7/1/2003 1.61% -12.86%

### 1.47% 2.54%4/1/2010 1.47% 2.80%1/3/2007 1.40% 2.00%

### 1.39% 6.93%8/1/2007 1.28% 8.61%

### 1.25% 4.59%7/2/2012 1.25% -2.04%2/2/2004 1.21% 2.33%8/1/2008 1.21% 0.49%4/3/2006 1.21% -0.12%5/3/2004 1.20% -4.08%6/2/2003 1.13% 2.94%3/1/2006 1.10% 2.61%2/1/2013 1.10% 1.85%5/1/2008 1.06% 2.09%3/1/2007 0.99% 3.06%9/1/2004 0.93% 3.32%

### 0.85% 5.38%3/3/2003 0.83% 7.38%

### 0.78% -3.62%### 0.75% 8.26%### 0.71% 0.95%### 0.70% -0.03%

9/1/2005 0.69% 0.64%3/3/2014 0.69% 0.48%4/1/2014 0.62% 4.48%

5/1/2001 0.51% -1.62%7/3/2006 0.51% 3.18%8/1/2002 0.49% 6.16%

### 0.40% -5.35%### 0.28% -1.66%

8/2/2004 0.23% 4.21%2/1/2006 0.05% 1.29%6/1/2009 0.02% 3.07%6/1/2006 0.01% 3.98%6/1/2005 -0.01% 7.86%

### -0.10% 2.16%3/1/2011 -0.10% 0.88%

### -0.23% -2.37%8/1/14 -0.29% 1.12%

### -0.50% 0.79%### -0.51% 3.29%

3/3/2008 -0.60% 1.77%4/2/2012 -0.75% 1.96%

### -0.87% 1.89%5/1/2002 -0.91% -17.27%7/1/2008 -0.99% 1.15%7/2/2001 -1.08% -1.02%8/1/2005 -1.13% -1.87%9/2/2003 -1.20% 4.20%5/2/2011 -1.36% 1.79%6/3/2013 -1.51% 0.86%7/1/2014 -1.52% -2.82%1/2/2002 -1.57% -11.85%7/3/2000 -1.65% 9.02%3/1/2004 -1.65% 2.86%4/1/2004 -1.69% -7.04%2/3/2003 -1.71% -21.34%

### -1.79% -9.70%6/1/2007 -1.80% -6.55%6/1/2011 -1.84% 0.43%3/1/2005 -1.93% 3.70%

### -2.00% 0.48%### -2.00% 1.39%

2/1/2000 -2.03% -16.42%4/1/2005 -2.03% 4.12%2/1/2002 -2.10% 2.01%7/1/2011 -2.17% -1.23%2/1/2007 -2.21% 0.98%5/1/2000 -2.22% 2.25%6/1/2001 -2.54% -15.87%1/3/2005 -2.56% 5.58%1/2/2003 -2.78% -13.76%4/3/2000 -3.13% 9.09%5/1/2006 -3.14% -2.04%8/1/2013 -3.18% -6.80%7/2/2007 -3.25% -7.21%7/1/2004 -3.49% 5.79%2/1/2008 -3.54% -4.97%1/2/2014 -3.62% 2.31%1/4/2010 -3.77% -4.04%

### -4.50% 4.33%8/2/2010 -4.86% 1.85%9/1/2000 -5.50% 13.66%6/1/2010 -5.54% 0.25%8/1/2011 -5.85% 3.06%

### -6.22% -1.03%1/2/2008 -6.31% -7.83%4/1/2002 -6.34% 1.40%5/1/2012 -6.47% 3.70%

8/1/2001 -6.63% 2.52%3/1/2001 -6.64% 4.77%9/1/2011 -7.45% 5.55%6/3/2002 -7.52% -2.90%

### -7.78% -3.66%7/1/2002 -8.23% -19.89%

### -8.35% 4.61%9/4/2001 -8.53% -3.77%5/3/2010 -8.55% -3.61%1/2/2009 -8.95% 0.94%6/2/2008 -8.99% -6.14%9/2/2008 -9.52% -0.05%2/1/2001 -9.68% 11.49%2/2/2009 -11.65% -10.23%9/3/2002 -11.66% -31.64%

### -18.56% -6.22%

Discrete Annual Compound Interest Use Solver when you have a function F(x) = yand you want to find x so that

Interest Rate y has a target value, or is at a maximum or minimum. 17.46%

you can also place contraints on range of xYear Cash Balance you can also solve when the function is on

0 $1,000.00 more than one variable: F(x1, x2) = y.1 $1,174.622 $1,379.73 use Solver to calculate3 $1,620.664 $1,903.65 (1) What discrete annual interest rate, at an initial balance of $1,000, 5 $2,236.07 results in $5,000 after 10 years?6 $2,626.53 (2) What initial balance, at an interest rate of 10%, 7 $3,085.17 results in $5,000 after 10 years?8 $3,623.90 (3) Challenge problem9 $4,256.70 Suppose you wanted to know: after how many years

10 $5,000.00 will $1000 at 7% be worth $5,000?Hint: this requires re-structuring the formula so that the changing number of years is located in one cell location See solution next sheet

Use Solver when you have a function F(x) = yand you want to find x so that y has a target value, or is at a maximum or minimum.

you can also place contraints on range of xyou can also solve when the function is on more than one variable: F(x1, x2) = y.

use Solver to calculate

(1) What discrete annual interest rate, at an initial balance of $1,000, results in $5,000 after 10 years? 17.46%(2) What initial balance, at an interest rate of 10%, results in $5,000 after 10 years? Answer: $1,927.72(3) Challenge problemSuppose you wanted to know: after how many years will $1000 at 7% be worth $5,000?Hint: this requires re-structuring the formula so that the changing number of years is located in one cell location See solution next sheet

(1) What discrete annual interest rate, at an initial balance of $1,000,

so that the changing number of years is located in one cell location

Discrete Annual Compound Interest

Interest Rate7.00%

Year Cash Balance After how many years will $1000 at 7% be worth $5,000?0 $1,000.001 $1,070.00 number of years 2 $1,144.903 $1,225.04 restated formula 4 $1,310.805 $1,402.55 $5,000.006 $1,500.737 $1,605.788 $1,718.199 $1,838.46

10 $1,967.15

After how many years will $1000 at 7% be worth $5,000?

number of years 23.78761

restated formula

(1+C4)^$G$8

Date Adj Close - RSP Adj Close - SPY5/1/2015 81.31 209.034/1/2015 80.73 206.383/2/2015 80.40 204.372/2/2015 81.18 207.631/2/2015 76.78 196.58

12/1/2014 79.09 202.5811/3/2014 78.87 203.1010/1/2014 76.82 197.679/2/2014 74.57 193.128/1/2014 76.55 195.827/1/2014 73.46 188.396/2/2014 75.22 190.955/1/2014 73.12 187.094/1/2014 71.58 182.853/3/2014 71.31 181.582/3/2014 70.88 180.091/2/2014 67.29 172.25

12/2/2013 69.34 178.5411/1/2013 67.39 174.0310/1/2013 65.93 169.029/3/2013 63.22 161.548/1/2013 60.73 156.597/1/2013 62.56 161.436/3/2013 59.22 153.505/1/2013 59.96 155.574/1/2013 58.39 151.983/1/2013 57.42 149.122/1/2013 55.02 143.661/2/2013 54.49 141.85

12/3/2012 51.16 134.9511/1/2012 50.03 133.7510/1/2012 49.40 133.009/4/2012 49.81 135.468/1/2012 48.58 132.117/2/2012 47.14 128.896/1/2012 47.08 127.385/1/2012 45.33 122.414/2/2012 48.74 130.233/1/2012 49.11 131.112/1/2012 48.00 127.021/3/2012 46.15 121.74

12/1/2011 43.67 116.34

11/1/2011 43.60 115.1410/3/2011 43.98 115.619/1/2011 38.90 104.238/1/2011 42.77 112.017/1/2011 45.67 118.526/1/2011 47.38 120.945/2/2011 48.25 123.024/1/2011 48.55 124.413/1/2011 47.08 120.912/1/2011 46.69 120.901/3/2011 44.89 116.84

12/1/2010 43.96 114.1811/1/2010 41.00 107.0210/1/2010 40.66 107.029/1/2010 39.27 103.098/2/2010 35.64 94.617/1/2010 37.41 99.076/1/2010 34.85 92.735/3/2010 37.20 97.794/1/2010 40.16 106.243/1/2010 39.12 104.622/1/2010 36.48 98.611/4/2010 35.02 95.63

12/1/2009 36.22 99.2411/2/2009 34.62 97.3810/1/2009 32.80 91.739/1/2009 34.06 93.528/3/2009 32.35 90.327/1/2009 30.62 87.106/1/2009 28.05 81.065/1/2009 28.39 81.114/1/2009 26.66 76.633/2/2009 22.46 69.712/2/2009 20.38 64.351/2/2009 22.95 72.09

12/1/2008 25.04 78.5411/3/2008 24.30 77.7810/1/2008 26.89 83.609/2/2008 33.99 100.148/1/2008 38.15 110.557/1/2008 37.05 108.876/2/2008 37.24 109.855/1/2008 41.30 119.87

4/1/2008 40.24 118.093/3/2008 38.06 112.722/1/2008 38.78 113.731/2/2008 39.98 116.75

12/3/2007 41.78 124.2611/1/2007 42.51 125.6810/1/2007 44.58 130.749/4/2007 44.08 128.998/1/2007 43.01 124.187/2/2007 42.98 122.616/1/2007 45.01 126.575/1/2007 45.86 128.454/2/2007 44.42 124.243/1/2007 42.55 118.972/1/2007 42.20 117.611/3/2007 42.40 119.96

12/1/2006 41.40 118.1811/1/2006 41.17 116.6210/2/2006 40.17 114.359/1/2006 38.71 110.858/1/2006 37.81 107.947/3/2006 36.80 105.636/1/2006 37.29 105.165/1/2006 37.40 104.894/3/2006 38.54 108.153/1/2006 38.21 106.802/1/2006 37.43 105.061/3/2006 37.30 104.47

12/1/2005 35.86 102.0211/1/2005 35.67 102.2110/3/2005 34.12 97.919/1/2005 35.06 100.288/1/2005 34.88 99.487/1/2005 35.19 100.426/1/2005 33.48 96.725/2/2005 32.97 96.584/1/2005 31.55 93.563/1/2005 32.60 95.352/1/2005 33.05 97.121/3/2005 32.36 95.14

12/1/2004 33.39 97.3211/1/2004 32.19 94.4710/1/2004 30.43 90.45

9/1/2004 29.72 89.308/2/2004 28.98 88.417/1/2004 29.01 88.196/1/2004 30.40 91.135/3/2004 29.50 89.474/1/2004 29.00 87.973/1/2004 29.70 89.662/2/2004 29.90 90.871/2/2004 29.34 89.65

12/1/2003 28.66 87.9111/3/2003 27.25 83.7010/1/2003 26.69 82.809/2/2003 24.96 78.598/1/2003 25.34 79.467/1/2003 24.29 77.856/2/2003 23.73 76.475/1/2003 23.53 75.67

Adj Close - Amazon Adj Close - Duke energy 429.23 74.90421.78 75.92372.10 75.15380.16 76.88354.53 84.48310.35 80.99338.64 78.43305.46 78.88322.44 71.79339.04 71.04312.99 68.49324.78 70.44312.55 67.49304.13 69.96336.37 66.89362.10 66.57358.69 65.60398.79 64.10393.62 64.98364.03 65.90312.64 61.36280.98 60.27301.22 64.51277.69 61.33269.20 60.82253.81 67.61266.49 65.26264.27 62.26265.50 61.12250.87 56.73252.05 56.74232.89 57.69254.32 56.90248.27 56.89233.30 58.85228.35 60.07212.91 57.25231.90 55.18202.51 54.10179.69 53.87194.44 54.23173.10 55.99

192.29 53.06213.51 51.34216.23 50.26215.23 47.54222.52 46.11204.49 46.68196.69 46.48195.81 45.65180.13 44.43173.29 44.04169.64 43.17180.00 43.01175.40 42.38165.23 43.39157.06 42.20124.83 40.93117.89 40.18109.26 37.59125.46 37.50137.10 38.87135.77 37.80118.40 37.87125.41 37.73134.52 39.29135.91 38.08118.81 35.5893.36 35.4081.19 34.8485.76 34.2883.66 32.3177.99 31.3480.52 30.0873.44 31.1964.79 29.3458.82 32.5051.28 32.2042.70 33.3857.24 34.6372.76 36.8580.81 36.8776.34 36.6973.33 36.2781.62 38.57

78.63 37.7771.30 36.8264.47 36.1877.70 38.0292.64 41.1190.56 40.3489.15 38.6493.15 37.6779.91 36.9678.54 33.9268.41 36.4569.14 38.9261.33 40.4539.79 40.0039.14 38.8037.67 38.4239.46 37.6540.34 35.9638.09 35.5132.12 33.8930.83 33.6726.89 33.6738.68 32.6234.61 31.3435.21 31.9936.53 32.0237.44 31.2044.82 30.8047.15 29.8348.46 29.1839.86 28.4345.30 31.3242.70 31.1345.15 31.7233.09 31.9235.51 29.5132.36 31.0334.27 29.7835.18 28.6943.22 28.1944.29 26.6639.68 26.6034.13 25.54

40.86 23.8338.14 23.0538.92 22.1154.40 20.8648.50 20.5043.60 21.3543.28 22.9143.01 22.2650.40 21.7652.62 20.4853.97 18.0654.43 17.8948.43 17.5546.32 16.8441.64 17.0336.32 19.3635.89 18.80

RSP SPY Amazon Duke Energy0.72% 1.28% 1.75% -1.35%0.41% 0.98% 12.53% 1.02%

-0.96% -1.58% -2.14% -2.28%5.57% 5.47% 6.98% -9.43%

-2.97% -3.01% 13.31% 4.22%0.28% -0.25% -8.72% 3.21%2.63% 2.71% 10.31% -0.57%2.98% 2.33% -5.41% 9.41%

-2.62% -1.39% -5.02% 1.05%4.12% 3.87% 7.99% 3.67%

-2.36% -1.35% -3.70% -2.82%2.82% 2.04% 3.84% 4.28%2.13% 2.29% 2.73% -3.59%0.38% 0.69% -10.08% 4.49%0.61% 0.83% -7.37% 0.48%5.20% 4.45% 0.95% 1.47%

-3.01% -3.59% -10.60% 2.31%2.84% 2.56% 1.30% -1.37%2.20% 2.92% 7.81% -1.41%4.19% 4.53% 15.22% 7.15%4.03% 3.12% 10.68% 1.78%

-2.96% -3.05% -6.96% -6.80%5.48% 5.04% 8.13% 5.06%

-1.24% -1.34% 3.11% 0.85%2.65% 2.33% 5.89% -10.58%1.68% 1.90% -4.88% 3.53%4.27% 3.73% 0.84% 4.71%0.96% 1.27% -0.46% 1.85%6.30% 4.99% 5.67% 7.46%2.24% 0.89% -0.47% -0.03%1.27% 0.56% 7.91% -1.65%

-0.83% -1.84% -8.80% 1.38%2.48% 2.50% 2.41% 0.02%3.02% 2.47% 6.22% -3.40%0.12% 1.18% 2.14% -2.04%3.79% 3.98% 7.00% 4.80%

-7.25% -6.19% -8.54% 3.69%-0.75% -0.67% 13.55% 1.98%2.29% 3.17% 11.96% 0.43%3.93% 4.25% -7.89% -0.68%5.53% 4.53% 11.63% -3.19%0.16% 1.04% -10.51% 5.37%

-0.88% -0.41% -10.47% 3.30%12.28% 10.36% -1.27% 2.13%-9.48% -7.19% 0.46% 5.55%-6.56% -5.65% -3.33% 3.06%-3.68% -2.02% 8.45% -1.23%-1.82% -1.70% 3.89% 0.43%-0.62% -1.13% 0.45% 1.80%3.08% 2.85% 8.35% 2.72%0.83% 0.01% 3.87% 0.89%3.94% 3.41% 2.13% 1.97%2.09% 2.30% -5.93% 0.39%6.97% 6.47% 2.59% 1.47%0.82% 0.00% 5.97% -2.35%3.50% 3.75% 5.07% 2.78%9.70% 8.58% 22.97% 3.04%

-4.87% -4.60% 5.72% 1.86%7.10% 6.61% 7.60% 6.65%

-6.51% -5.31% -13.83% 0.25%-7.65% -8.28% -8.87% -3.58%2.62% 1.54% 0.97% 2.78%6.97% 5.91% 13.69% -0.18%4.10% 3.07% -5.75% 0.36%

-3.37% -3.70% -7.01% -4.03%4.51% 1.89% -1.03% 3.13%5.39% 5.98% 13.45% 6.78%

-3.77% -1.94% 24.11% 0.51%5.15% 3.48% 13.97% 1.60%5.49% 3.63% -5.48% 1.62%8.79% 7.20% 2.48% 5.92%

-1.20% -0.07% 7.02% 3.06%6.26% 5.68% -3.19% 4.08%

17.14% 9.47% 9.20% -3.63%9.75% 8.00% 12.53% 6.12%

-11.91% -11.37% 9.67% -10.23%-8.71% -8.57% 13.72% 0.93%3.04% 0.97% 18.31% -3.60%

-10.13% -7.21% -29.31% -3.67%-23.45% -18.05% -23.99% -6.21%-11.54% -9.89% -10.49% -0.06%

2.92% 1.53% 5.69% 0.50%-0.50% -0.90% 4.02% 1.14%

-10.36% -8.73% -10.71% -6.14%2.62% 1.50% 3.73% 2.10%

5.57% 4.66% 9.79% 2.54%-1.87% -0.90% 10.07% 1.75%-3.06% -2.62% -18.67% -4.95%-4.40% -6.24% -17.59% -7.84%-1.72% -1.13% 2.27% 1.90%-4.76% -3.95% 1.57% 4.31%1.11% 1.35% -4.39% 2.54%2.46% 3.80% 15.33% 1.89%0.08% 1.28% 1.73% 8.60%

-4.62% -3.18% 13.81% -7.19%-1.87% -1.47% -1.06% -6.56%3.18% 3.34% 11.99% -3.87%4.31% 4.33% 43.27% 1.13%0.82% 1.15% 1.65% 3.05%

-0.48% -1.98% 3.83% 0.98%2.38% 1.49% -4.64% 2.01%0.56% 1.33% -2.21% 4.59%2.46% 1.97% 5.74% 1.26%3.69% 3.10% 17.05% 4.66%2.37% 2.66% 4.10% 0.66%2.70% 2.16% 13.67% 0.00%

-1.34% 0.45% -36.36% 3.18%-0.28% 0.26% 11.12% 3.99%-3.01% -3.06% -1.72% -2.06%0.86% 1.26% -3.68% -0.10%2.08% 1.64% -2.46% 2.61%0.34% 0.57% -17.99% 1.28%3.95% 2.37% -5.07% 3.23%0.53% -0.19% -2.74% 2.17%4.45% 4.30% 19.54% 2.62%

-2.72% -2.39% -12.79% -9.68%0.50% 0.80% 5.91% 0.62%

-0.88% -0.94% -5.58% -1.88%4.98% 3.75% 31.08% -0.64%1.53% 0.15% -7.06% 7.87%4.40% 3.17% 9.29% -5.05%

-3.25% -1.89% -5.73% 4.13%-1.37% -1.85% -2.62% 3.71%2.11% 2.07% -20.58% 1.76%

-3.13% -2.27% -2.45% 5.60%3.64% 2.97% 10.99% 0.20%5.63% 4.36% 15.07% 4.10%2.35% 1.28% -18.00% 6.92%

2.54% 1.00% 6.89% 3.33%-0.10% 0.24% -2.02% 4.17%-4.68% -3.27% -33.49% 5.79%2.99% 1.83% 11.48% 1.74%1.73% 1.70% 10.65% -4.05%

-2.39% -1.91% 0.74% -7.06%-0.68% -1.33% 0.63% 2.87%1.89% 1.35% -15.86% 2.30%2.34% 1.96% -4.31% 6.07%5.05% 4.91% -2.53% 12.54%2.09% 1.09% -0.85% 0.96%6.69% 5.21% 11.68% 1.89%

-1.49% -1.10% 4.45% 4.19%4.22% 2.04% 10.65% -1.13%2.33% 1.79% 13.67% -12.82%0.86% 1.06% 1.19% 2.90%

Copyright Daniel Egger/ Attribution 4.0 International (CC BY 4.0)

Copyright Daniel Egger/ Attribution 4.0 International (CC BY 4.0)

Copyright Daniel Egger/ Attribution 4.0 International (CC BY 4.0)

2S-1, 2S-2 Cell Refs and Charts2S-3 Arithmetic in Excel2S-4 Functions on Cells2S-5, 2S-6 Functions on Arrays2S-7 Sorting Data2S-8 Solver Plugin2S-9 Solver Challenge2S-10 rsp vs spycopyright