CALCULATING FUTURE VALUES WITH EXCELInitial Deposit 100Interest Rate 6%Number of years, n 2

Account balance after n years 112.36

Year Future Value0 $100.001 $106.002 $112.363 $119.104 $126.255 $133.826 $141.857 $150.368 $159.389 $168.95

10 $179.0811 $189.8312 $201.2213 $213.2914 $226.0915 $239.6616 $254.0417 $269.2818 $285.4319 $302.5620 $320.71

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21$0.00

$50.00

$100.00

$150.00

$200.00

$250.00

$300.00

$350.00

Future Value of $100 at 6% Annual Interest

Fut

ure

Val

ue

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21$0.00

$50.00

$100.00

$150.00

$200.00

$250.00

$300.00

$350.00

Future Value of $100 at 6% Annual Interest

Fut

ure

Val

ue

Initial Deposit 100 100 100Interest Rate 0% 6% 12%

Year FV at 0% FV at 6% FV at 12%0 100 100.00 100.001 100 106.00 112.002 100 112.36 125.443 100 119.10 140.494 100 126.25 157.355 100 133.82 176.236 100 141.85 197.387 100 150.36 221.078 100 159.38 247.609 100 168.95 277.31

10 100 179.08 310.5811 100 189.83 347.8512 100 201.22 389.6013 100 213.29 436.3514 100 226.09 488.7115 100 239.66 547.3616 100 254.04 613.0417 100 269.28 686.6018 100 285.43 769.0019 100 302.56 861.2820 100 320.71 964.63

FUTURE VALUE OF A SINGLE DEPOSIT AT DIFFERENT INTEREST RATES

HOW $100 AT TIME 0 GROWS AT 0%, 6%, 12%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210

200

400

600

800

1000

1200

FV at 0%

FV at 6%

FV at 12%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 210

200

400

600

800

1000

1200

FV at 0%

FV at 6%

FV at 12%

Interest 6%

Year

1 0 100.00 6 $ 106.00 2 106.00 100.00 12.36 $ 218.36 3 218.36 100.00 19.10 $ 337.46 4 337.46 100.00 26.25 $ 463.71 5 463.71 100.00 33.82 $ 597.53 6 597.53 100.00 41.85 $ 739.38 7 739.38 100.00 50.36 $ 889.75 8 889.75 100.00 59.38 $ 1,049.13 9 1049.13 100.00 68.95 $ 1,218.08

10 1218.08 100.00 79.08 $ 1,397.16

$1,397.16

FUTURE VALUE WITH ANNUAL DEPOSITS at the beginning of year

Account balance, beginning of year

Deposit at beginning of year

Interest earned during year

Total in account at end of year

Future Value using Excel's FV functions

Interest 6%

Year

1 0 100.00 0 $ 100.00 2 100.00 100.00 6.00 $ 206.00 3 206.00 100.00 12.36 $ 318.36 4 318.36 100.00 19.10 $ 437.46 5 437.46 100.00 26.25 $ 563.71 6 563.71 100.00 33.82 $ 697.53 7 697.53 100.00 41.85 $ 839.38 8 839.38 100.00 50.36 $ 989.75 9 989.75 100.00 59.38 $ 1,149.13

10 1149.13 100.00 68.95 $ 1,318.08

$1,318.08

FUTURE VALUE WITH ANNUAL DEPOSITS at the end of year

Account balance, end of year

Deposit at end of year

Interest earned during year

Total in account at end of year

Future Value using Excel's FV functions

Future Payment (X) 100Time of future payment (n) 3interest rate(,r) 6%

83.96193

Discount rate0% 100.001% 97.062% 94.233% 91.514% 88.905% 86.386% 83.967% 81.638% 79.389% 77.22

10% 75.1311% 73.1212% 71.1813% 69.3114% 67.5015% 65.7516% 64.0717% 62.4418% 60.8619% 59.3420% 57.8721% 56.4522% 55.0723% 53.7424% 52.4525% 51.2026% 49.9927% 48.8228% 47.6829% 46.5830% 45.5231% 44.4832% 43.4833% 42.5134% 41.56

THE PRESENT VALUE OF $100 IN 3 YEARS in this example we vary the discount rate r

Present Value (X/(1+r)n)

Present Value

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 510.00

20.00

40.00

60.00

80.00

100.00

120.00

Present Value of $100 to be paid in 3 Years wen Discount Rate Varies

Discount Rate

Present Value

35% 40.6436% 39.7537% 38.8938% 38.0539% 37.2440% 36.4441% 35.6742% 34.9243% 34.2044% 33.4945% 32.8046% 32.1347% 31.4848% 30.8549% 30.2350% 29.63

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 510.00

20.00

40.00

60.00

80.00

100.00

120.00

Present Value of $100 to be paid in 3 Years wen Discount Rate Varies

Discount Rate

Present Value

CALCULATING PRESENT VALUES WITH EXCEL

Annual Payment 100r, interest rate 6%

Year1 100 94.339622642 100 88.9996443 100 83.96192834 100 79.209366325 100 74.72581729

Present value of all paymentsSumming the present value $421.24Using Excel's PV function $421.24

Using Excel's NPV function $421.24

Payment at end of

year

Present value of payment

CALCULATING NET PRESENT VALUE (NPV) WITH EXCELr, interest rate 6%

Year1 100 $94.342 200 $178.003 300 $251.894 400 $316.845 500 $373.63

Present value of all paymentsSumming the present values $1,214.69Using Excel's NPV function $1,214.69

Payment at end of year

Prsent value

CALCULATING NET PRESENT VALUE (NPV) WITH EXCELr, interest rate 5%

Year Payment Present Value0 -800 -800.001 100 95.242 150 136.053 200 172.774 250 205.685 300 235.06

NPVSumming the present values $44.79Using Excel's NPV function $44.79

Discount Rate NPV0% 200.001% 165.862% 133.363% 102.414% 72.925% 44.796% 17.967% -7.658% -32.119% -55.48

10% -77.8311% -99.2112% -119.6713% -139.2614% -158.0415% -176.0316% -193.28

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16%

-250.00

-200.00

-150.00

-100.00

-50.00

0.00

50.00

100.00

150.00

200.00

250.00

NPV and the Discount Rate

Discount Rate

NPV

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16%

-250.00

-200.00

-150.00

-100.00

-50.00

0.00

50.00

100.00

150.00

200.00

250.00

NPV and the Discount Rate

Discount Rate

NPV

USING NPV TO CHOOSE BETWEEN INVESTMENTS

Discount Rate 15%

Year Investment A Investment B0 -800 -8001 250 6002 500 2003 200 1004 250 5005 300 300

NPV 219.06 373.75

CALCULATING THE IRR WITH EXCELr, interest rate 6.6965%

Year Payment0 -8001 1002 1503 2004 2505 300

NPV 0.00IRR 6.6965%

Discount Rate NPV0% 200.001% 165.862% 133.363% 102.414% 72.925% 44.796% 17.967% -7.658% -32.119% -55.48

10% -77.8311% -99.2112% -119.6713% -139.2614% -158.0415% -176.0316% -193.28

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16%

-250.00

-200.00

-150.00

-100.00

-50.00

0.00

50.00

100.00

150.00

200.00

250.00

NPV and the Discount Rate

Discount Rate

NPV

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16%

-250.00

-200.00

-150.00

-100.00

-50.00

0.00

50.00

100.00

150.00

200.00

250.00

NPV and the Discount Rate

Discount Rate

NPV

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16%

-250.00

-200.00

-150.00

-100.00

-50.00

0.00

50.00

100.00

150.00

200.00

250.00

NPV and the Discount Rate

Discount Rate

NPV

HELPING MARIO SAVE FOR A CAR

Deposit, X 8903.133Interest rate 8.00%

Year

0 0 8903.133 8903.133 $9,615.38 1 $9,615.38 8903.133 $18,518.52 $20,000.00 2 $20,000.00 -20000 ($0.00) ($0.00)

0.00

Deposit, X 8903.13Interest rate 8.00%

Year

0 0 8903.13 8903.1339 $9,615.38 1 $9,615.38 8903.13 $18,518.52 $20,000.00 2 $20,000.00 -20000 $0.00 $0.00

0.00

Goal $20,000.00When to reach the goal? 5Interest rate 6.00%Deposit, X $3,347.10

In bank, before deposit

Deposit or

withdrawl

Total at beginning

of year

End of year with interest

NPV of all deposits and payments

HELPING MARIO SAVE FOR A CAR USING AN EXCEL FUNCTION GOAL SEEK

In bank, before deposit

Deposit or

withdrawl

Total at beginning

of year

End of year with interest

NPV of all deposits and payments

HELPING MARIO SAVE FOR A CAR using Excel's PV function

SAVING FOR COLLEGE

Interest rate 8.00%Annual deposit $4,000.000Annual cost of deposit $20,000.00

Birthday Total10 0 $4,000.00 4,000.00 11 $4,320.00 $4,000.00 8,320.00 12 $8,985.60 $4,000.00 12,985.60 13 $14,024.45 $4,000.00 18,024.45 14 $19,466.40 $4,000.00 23,466.40 15 $25,343.72 $4,000.00 29,343.72 16 $31,691.21 $4,000.00 35,691.21 17 $38,546.51 $4,000.00 42,546.51 18 $45,950.23 -$20,000.00 25,950.23 19 $28,026.25 -$20,000.00 8,026.25 20 $8,668.35 -$20,000.00 (11,331.65)21 ($12,238.18) -$20,000.00 (32,238.18)

NPV of all payments -$13,826.40

SAVING FOR COLLEGE USING TRIAL AND ERROR

Interest rate 8.00%Annual deposit $6,227.78Annual cost of deposit -$20,000.00

Birthday Total10 0 $6,227.78 6,227.78 11 $6,726.00 $6,227.78 12,953.77 12 $13,990.07 $6,227.78 20,217.85 13 $21,835.28 $6,227.78 28,063.05 14 $30,308.10 $6,227.78 36,535.87 15 $39,458.74 $6,227.78 45,686.52 16 $49,341.44 $6,227.78 55,569.21 17 $60,014.75 $6,227.78 66,242.52 18 $71,541.93 -$20,000.00 51,541.93 19 $55,665.28 -$20,000.00 35,665.28 20 $38,518.50 -$20,000.00 18,518.50 21 $19,999.98 -$20,000.00 (0.02)

In bank on birthday, before

deposit/withdrawl

Deposit or withdrawl at

beginning of year

In bank on birthday, before

deposit/withdrawl

Deposit or withdrawl at

beginning of year

NPV of all payments -$0.01

Interest rate 8.00%Annual deposit $6,227.78Annual cost of deposit -$20,000.00

Birthday Total10 0 $6,227.78 6,227.78 11 $6,726.00 $6,227.78 12,953.77 12 $13,990.08 $6,227.78 20,217.85 13 $21,835.28 $6,227.78 28,063.06 14 $30,308.10 $6,227.78 36,535.88 15 $39,458.75 $6,227.78 45,686.52 16 $49,341.45 $6,227.78 55,569.22 17 $60,014.76 $6,227.78 66,242.54 18 $71,541.94 -$20,000.00 51,541.94 19 $55,665.29 -$20,000.00 35,665.29 20 $38,518.52 -$20,000.00 18,518.52 21 $20,000.00 -$20,000.00 -

NPV of all payments $0.00

SAVING FOR COLLEGE USING EXCEL FORMUALS ONLYLinda's age when plan started 10Linda's age at last deposit 17Number of deposits 8Number of withdrawls 4Annual cost of college $20,000.00Interest rate 8.00%

Annual deposit $6,227.78

Linda's age today0 $1,768.811 $1,962.732 $2,184.473 $2,439.68

SAVING FOR COLLEGE USING GOAL SEEK

In bank on birthday, before

deposit/withdrawl

Deposit or withdrawl at

beginning of year

Annual amount deposited

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16$0

$5,000

$10,000

$15,000

$20,000

$25,000

Annual Deposit Required to Fun 4 Years of $20,000

When Linda is 18

Linda's age at start of plan

4 $2,735.615 $3,081.726 $3,490.657 $3,979.618 $4,572.699 $5,304.68

10 $6,227.7811 $7,423.9612 $9,029.8813 $11,291.4714 $14,700.6015 $20,404.92

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16$0

$5,000

$10,000

$15,000

$20,000

$25,000

Annual Deposit Required to Fun 4 Years of $20,000

When Linda is 18

Linda's age at start of plan

SAVING FOR COLLEGE SAVING FOR COLLEGE

Interest rate 9.00%Annual deposit $75,000.000Annual cost of deposit $30,000.00

Birthday Total$4,320.00 1 0 $75,000.00 75,000.00 $81,750.00 $8,985.60 2 $81,750.00 81,750.00 $97,127.18

$14,024.45 3 $97,127.18 97,127.18 $115,396.80 $19,466.40 4 $115,396.80 115,396.80 $137,102.93 $25,343.72 5 $137,102.93 137,102.93 $162,892.00 $31,691.21 6 $162,892.00 162,892.00 $193,531.98 $38,546.51 7 $193,531.98 -$30,000.00 163,531.98 $194,292.35 $45,950.23 8 $194,292.35 -$30,000.00 164,292.35 $195,195.74 $28,026.25 9 $195,195.74 -$30,000.00 165,195.74 $196,269.05

$8,668.35 10 $196,269.05 -$30,000.00 166,269.05 $197,544.26 ($12,238.18)($34,817.24)

NPV of all pa -$22,191.60

SAVING FOR COLLEGE USING TRIAL AND ERROR

$6,726.00 $13,990.07 $21,835.28 $30,308.10 $39,458.74 $49,341.44 $60,014.75 $71,541.93 $55,665.28 $38,518.50 $19,999.98

($0.02)

End of year with interest

In bank on birthday,

before deposit/withd

rawl

Deposit or withdrawl

at beginning of year

End of year with

interest

End of year with interest

$6,726.00 $13,990.08 $21,835.28 $30,308.10 $39,458.75 $49,341.45 $60,014.76 $71,541.94 $55,665.29 $38,518.52 $20,000.00

$0.00

SAVING FOR COLLEGE USING EXCEL FORMUALS ONLY

End of year with interest

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16$0

$5,000

$10,000

$15,000

$20,000

$25,000

Annual Deposit Required to Fun 4 Years of $20,000

When Linda is 18

Linda's age at start of plan

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16$0

$5,000

$10,000

$15,000

$20,000

$25,000

Annual Deposit Required to Fun 4 Years of $20,000

When Linda is 18

Linda's age at start of plan

89107.597127.17

105868.62115396.79

125782.5104402.93

81099.1955698.12

SAVING FOR RETIREMENT

Joe's age today 20Joe's age at last deposit 64Number of deposits 45Number of withdrawls 20Annual withdrawal from age 65 $ 100,000.00 Interest rate 8.00%

Annual deposit $ 2,540.23

Joe's age today Annual amount deposited20 2,540.2321 2,750.5722 2,978.9623 3,227.0724 3,496.7325 3,789.9626 4,109.0227 4,456.3928 4,834.8529 5,247.4830 5,697.7331 6,189.4732 6,727.0333 7,315.3234 7,959.8535 8,666.9036 9,443.6237 10,298.1638 11,239.9139 12,279.6840 13,430.0341 14,705.5842 16,123.5343 17,704.1544 19,471.6045 21,454.8246 23,688.8647 26,216.5148 29,090.6149 32,377.1850 36,159.7951 40,545.8652 45,675.7953 51,736.7454 58,983.8455 67,774.17

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 642,000.00

22,000.00

42,000.00

62,000.00

82,000.00

102,000.00

122,000.00

142,000.00

162,000.00

182,000.00

202,000.00

222,000.00

242,000.00

262,000.00

282,000.00

302,000.00

322,000.00

342,000.00

362,000.00

382,000.00

402,000.00

422,000.00

442,000.00

462,000.00

482,000.00

502,000.00

522,000.00

542,000.00

562,000.00

582,000.00

602,000.00

622,000.00

642,000.00

662,000.00

682,000.00

702,000.00

722,000.00

742,000.00

762,000.00

782,000.00

802,000.00

822,000.00

842,000.00

862,000.00

882,000.00

902,000.00

922,000.00

942,000.00

962,000.00

982,000.00

Annual Deposit Required to Fund 20 Years of $100,000When Joe is 65

Joe's age at start of plan

56 78,623.4457 92,305.0858 110,034.3459 133,836.4660 167,356.6661 217,885.1262 302,431.8463 472,026.3264 981,814.74

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 642,000.00

22,000.00

42,000.00

62,000.00

82,000.00

102,000.00

122,000.00

142,000.00

162,000.00

182,000.00

202,000.00

222,000.00

242,000.00

262,000.00

282,000.00

302,000.00

322,000.00

342,000.00

362,000.00

382,000.00

402,000.00

422,000.00

442,000.00

462,000.00

482,000.00

502,000.00

522,000.00

542,000.00

562,000.00

582,000.00

602,000.00

622,000.00

642,000.00

662,000.00

682,000.00

702,000.00

722,000.00

742,000.00

762,000.00

782,000.00

802,000.00

822,000.00

842,000.00

862,000.00

882,000.00

902,000.00

922,000.00

942,000.00

962,000.00

982,000.00

Annual Deposit Required to Fund 20 Years of $100,000When Joe is 65

Joe's age at start of plan

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 642,000.00

22,000.00

42,000.00

62,000.00

82,000.00

102,000.00

122,000.00

142,000.00

162,000.00

182,000.00

202,000.00

222,000.00

242,000.00

262,000.00

282,000.00

302,000.00

322,000.00

342,000.00

362,000.00

382,000.00

402,000.00

422,000.00

442,000.00

462,000.00

482,000.00

502,000.00

522,000.00

542,000.00

562,000.00

582,000.00

602,000.00

622,000.00

642,000.00

662,000.00

682,000.00

702,000.00

722,000.00

742,000.00

762,000.00

782,000.00

802,000.00

822,000.00

842,000.00

862,000.00

882,000.00

902,000.00

922,000.00

942,000.00

962,000.00

982,000.00

Annual Deposit Required to Fund 20 Years of $100,000When Joe is 65

Joe's age at start of plan

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 642,000.00

22,000.00

42,000.00

62,000.00

82,000.00

102,000.00

122,000.00

142,000.00

162,000.00

182,000.00

202,000.00

222,000.00

242,000.00

262,000.00

282,000.00

302,000.00

322,000.00

342,000.00

362,000.00

382,000.00

402,000.00

422,000.00

442,000.00

462,000.00

482,000.00

502,000.00

522,000.00

542,000.00

562,000.00

582,000.00

602,000.00

622,000.00

642,000.00

662,000.00

682,000.00

702,000.00

722,000.00

742,000.00

762,000.00

782,000.00

802,000.00

822,000.00

842,000.00

862,000.00

882,000.00

902,000.00

922,000.00

942,000.00

962,000.00

982,000.00

Annual Deposit Required to Fund 20 Years of $100,000When Joe is 65

Joe's age at start of plan

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 642,000.00

22,000.00

42,000.00

62,000.00

82,000.00

102,000.00

122,000.00

142,000.00

162,000.00

182,000.00

202,000.00

222,000.00

242,000.00

262,000.00

282,000.00

302,000.00

322,000.00

342,000.00

362,000.00

382,000.00

402,000.00

422,000.00

442,000.00

462,000.00

482,000.00

502,000.00

522,000.00

542,000.00

562,000.00

582,000.00

602,000.00

622,000.00

642,000.00

662,000.00

682,000.00

702,000.00

722,000.00

742,000.00

762,000.00

782,000.00

802,000.00

822,000.00

842,000.00

862,000.00

882,000.00

902,000.00

922,000.00

942,000.00

962,000.00

982,000.00

Annual Deposit Required to Fund 20 Years of $100,000When Joe is 65

Joe's age at start of plan

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 642,000.00

22,000.00

42,000.00

62,000.00

82,000.00

102,000.00

122,000.00

142,000.00

162,000.00

182,000.00

202,000.00

222,000.00

242,000.00

262,000.00

282,000.00

302,000.00

322,000.00

342,000.00

362,000.00

382,000.00

402,000.00

422,000.00

442,000.00

462,000.00

482,000.00

502,000.00

522,000.00

542,000.00

562,000.00

582,000.00

602,000.00

622,000.00

642,000.00

662,000.00

682,000.00

702,000.00

722,000.00

742,000.00

762,000.00

782,000.00

802,000.00

822,000.00

842,000.00

862,000.00

882,000.00

902,000.00

922,000.00

942,000.00

962,000.00

982,000.00

Annual Deposit Required to Fund 20 Years of $100,000When Joe is 65

Joe's age at start of plan

LOAN PAYMENT

Loan Principal 100,000.00Loan Interest 10.00%Years to pay off loan 10Annual payment $16,274.54

$16,274.54

Year1 100,000.00 $16,274.54 $10,000.00 $6,274.54 2 $93,725.46 $16,274.54 $9,372.55 $6,901.99 3 $86,823.47 $16,274.54 $8,682.35 $7,592.19 4 $79,231.27 $16,274.54 $7,923.13 $8,351.41 5 $70,879.86 $16,274.54 $7,087.99 $9,186.55 6 $61,693.31 $16,274.54 $6,169.33 $10,105.21 7 $51,588.10 $16,274.54 $5,158.81 $11,115.73 8 $40,472.37 $16,274.54 $4,047.24 $12,227.30 9 $28,245.07 $16,274.54 $2,824.51 $13,450.03

10 $14,795.04 $16,274.54 $1,479.50 $14,795.04

HOW LONG TO PAY OFF THIS LOAN?

Loan amount $1,000.00Interest rate 10.00%Annual payment $250.00

Year Interest1 $1,000.00 $250.00 $100.00 $150.002 $850.00 $250.00 $85.00 $165.003 $685.00 $250.00 $68.50 $181.504 $503.50 $250.00 $50.35 $199.655 $303.85 $250.00 $30.39 $219.626 $84.24 $250.00 $8.42 $241.58

Principal at beginning of

yearPrincipal at end of year

Part of payment that

is interest

Part of payment that is principal

Principal at beginning of

yearPayment at end of year

Return of principal

MERCK & CO. 1991-2000

Year Dividends

1991 893 184 481992 1,064 863 521993 1,174 371 831994 1,434 705 1391995 1,540 1,571 2641996 1,729 2,493 4421997 2,040 2,573 4131998 2,253 3,626 4901999 2,590 3,582 3232000 2,798 3,545 641

Purchase of

Treasury stock

Proceeds from

exercise of stock options

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 20010

500

1,000

1,500

2,000

2,500

3,000

Merck Dividends, 1991-2000

Year

Div

iden

ds

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 20010

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

Merck Treasury Stock and Option Exercise

Purchase of Treasury stockProceeds from exercise of stock options

Years

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 20010

500

1,000

1,500

2,000

2,500

3,000

Merck Dividends, 1991-2000

Year

Div

iden

ds

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 20010

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

Merck Treasury Stock and Option Exercise

Purchase of Treasury stockProceeds from exercise of stock options

Years

Line versus XY Chartsx y0 136 228 31

15 -822 1497 6

0 6 8 15 22 97

-10

-5

0

5

10

15

20

25

30

35

y

y

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

-10

-5

0

5

10

15

20

25

30

35

x

0 6 8 15 22 97

-10

-5

0

5

10

15

20

25

30

35

y

y

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

-10

-5

0

5

10

15

20

25

30

35

x

AVERAGE MONTHLY MAXIMUM AND MINIMUM TEMPERATURES--NEW YORK CITYJan Feb Mar Apr May Jun Jul Aug Sep

38 40 50 61 72 80 85 84 76

25 27 35 44 54 63 68 67 60

Avg max temp (F)

Avg min temp (F)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

102030405060708090

NYC Temprature

Avg max temp (F)Avg min temp (F)

Months

AVERAGE MONTHLY MAXIMUM AND MINIMUM TEMPERATURES--NEW YORK CITYOct Nov Dec

65 54 43

50 41 31

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

102030405060708090

NYC Temprature

Avg max temp (F)Avg min temp (F)

Months

GRAPHS TITLES THAT UPDATE AUTOMATICALLYGrowth 15%

Year Cash flow1 1002 115.003 132.254 152.095 174.906 201.147 231.31

Cash Flow Graph When Growth = 15.0%

1 2 3 4 5 6 70

50

100

150

200

250

Cash Flow Graph When Growth = 15.0%

1 2 3 4 5 6 70

50

100

150

200

250

Cash Flow Graph When Growth = 15.0%

EXERCISE 1Future Value, FV

Deposit $ 600.00 Interest rate, r 15%Number of years, n 10Future Value, FV $2,427.33

YEAR FUTURE VALUE1 $690.00 2 $793.50 3 $912.52 4 $1,049.40 5 $1,206.81 6 $1,387.84 7 $1,596.01 8 $1,835.41 9 $2,110.73

10 $2,427.33

EXERCISE 2

Interest rate 8.00%

Year Gift

0 10000 $21,589.25 1 10000 $19,990.05 2 10000 $18,509.30 3 10000 $17,138.24 4 10000 $15,868.74 5 10000 $14,693.28 6 10000 $13,604.89 7 10000 $12,597.12 8 10000 $11,664.00 9 10000 $10,800.00

TOTAL $156,454.87 Future value in year 10 $156,454.87

EXERCISE 3

Interest rate 7.00%

Year Gift

Future value in year 10

Future value in year 10

1 2 3 4 5 6 7 8 9 10$0.00

$250.00 $500.00 $750.00

$1,000.00 $1,250.00 $1,500.00 $1,750.00 $2,000.00 $2,250.00 $2,500.00

FUTURE VALUE, FV

YEARS

FUTU

RE V

ALUE

0 10000 $7,628.95 1 10000 $8,162.98 2 10000 $8,734.39 3 10000 $9,345.79

TOTAL $33,872.11 Present Value of as of today $33,872.11

EXERCISE 4

Interest rate 14.00%

Year Gift

1 1000 $592.08 2 1000 $674.97 3 1000 $769.47 4 1000 $877.19

TOTAL $2,913.71 Present Value of as of today $2,913.71

EXERCISE 5

Year Payment0 -10001 1502 1503 1504 1505 1506 1507 1508 1509 150

10 15011 15012 15013 15014 15015 150

USING IRR EXCEL FUNCTION 12%USING RATE EXCEL FUNCTION 12%

Future value in year 10

EXERCISE 6

Year Payment0 -10001 1002 2003 3004 4005 5006 6007 7008 8009 900

10 1000

USING IRR EXCEL FUNCTION 32%

EXERCISE 7

BOND FACE VALUE $ 1,000.00 NUMBER OF PAYMENTS 6PAYMENTS $ 120.00 INTEREST RATE 7.00%PV $ 1,238.33

SAVING FOR THE FUTUREYour age today 35Retirement age 65Number of deposits 30Planned age of demise 85Number of withdrawls 20Annual desired pension payout 100,000Annual payment 10,733 Interest rate 8%

Your age55 10,733 10,733 56575859

Account balance, beginning of year

Deposit orwithdrawalbeginning of

year

Interest earned

during year

60616263646566676869707172737475767778798081828384

SAVING FOR THE FUTURE

Total in account

end of year