1

There are two main methods for computing interest. Do you know the difference between them? Do you know what difference it makes in a savings account after a period

of some years?

What is the difference between simple and compound interest and does it really matter?

Simple versus Compound Interest

Module gtf1

Prepared for SSAC byGary Franchy – Davenport University

© The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved. 2005

Quantitative concepts and skillsArithmetic GrowthGeometric GrowthForward ModelingFunction, linearFunction, exponentialGraph, XY (scatter)

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Simple interest is an example of arithmetic growth where the amount of interest generated each term is constant; it is based on only the starting amount. Year to year there is a constant difference in the value of the savings account, and so the successive values track a linear function. Compound interest is an example of geometric growth where the amount of interest generated each term increases because it is based on both the starting amount and the previously earned interest. Year to year there is a constant ratio of the values in the savings account, and so the successive values track an exponential function. Accordingly, compound interest is commonly said to exhibit exponential growth,

Overview of Module

Slides 3-4 ask you to set up your worksheet and format the cells.

Slides 5-9 have you computing simple and compound interest for a set period of time and interest rate. You will perform the calculation, graph the increasing savings accounts, and draw trendlines through the plotted functions for the linearly increasing and geometrically increasing values.

Slides 10-12 ask you to calculate the difference between the two types of accounts using a variety of interest rates.

Slides 13-14 give the assignment to hand in.

3

What is the difference in results between savings accounts that use simple and compound interest when you invest $100,000 at 8% for 25 years?

Recreate this spreadsheet

= Cell with a number in it

= Cell with a formula in it

B C D E F G2 Present Value = 100000 Year Simple Compound3 Interest Rate = 8% 14 25 36 47 58 69 710 811 912 1013 1114 1215 1316 1417 1518 1619 1720 1821 1922 2023 2124 2225 2326 2427 25

One way to answer the question with a spreadsheet is to lay it out

year by year.

Type in the “%” symbol when entering percents; otherwise you must enter the decimal form.

Question 1

4

B C D E F G2 Present Value = $100,000 Year Simple Compound3 Interest Rate = 8% 14 25 36 47 58 69 7

10 811 912 1013 1114 1215 1316 1417 1518 1619 1720 1821 1922 2023 2124 2225 2326 2427 25

To format cells:1. Select the cells.2. Right-click the mouse.3. Select “Format Cells”.4. Choose “Number” tab.5. Choose “Currency”.6. Adjust “Decimal Places” to

the desired number of places.

7. Select “OK”.

Question 1

Format these cells as currency rounded to the nearest dollar.

5

B C D E F G2 Present Value = $100,000 Year Simple Compound3 Interest Rate = 8% 14 25 36 47 58 69 7

10 811 912 1013 1114 1215 1316 1417 1518 1619 1720 1821 1922 2023 2124 2225 2326 2427 25

Compute the results for future value for each year in the column labeled “Simple”.

The Simple Interest Formula:

WhereFV = Future Value ($)PV = Present Value ($)r = Interest Ratet = Time (Years)

rtPVFV 1

Question 1

6

B C D E F G2 Present Value = $100,000 Year Simple Compound3 Interest Rate = 8% 1 $108,0004 2 $116,0005 3 $124,0006 4 $132,0007 5 $140,0008 6 $148,0009 7 $156,000

10 8 $164,00011 9 $172,00012 10 $180,00013 11 $188,00014 12 $196,00015 13 $204,00016 14 $212,00017 15 $220,00018 16 $228,00019 17 $236,00020 18 $244,00021 19 $252,00022 20 $260,00023 21 $268,00024 22 $276,00025 23 $284,00026 24 $292,00027 25 $300,000

Compute the results for future value for each year in the column labeled “Compound”.

The Compound Interest Formula:

WhereFV = Future Value ($)PV = Present Value ($)r = Interest Ratet = Time (Years)

trPVFV 1

Question 1

7

B C D E F G2 Present Value = $100,000 Year Simple Compound3 Interest Rate = 8% 1 $108,000 $108,0004 2 $116,000 $116,6405 3 $124,000 $125,9716 4 $132,000 $136,0497 5 $140,000 $146,9338 6 $148,000 $158,6879 7 $156,000 $171,382

10 8 $164,000 $185,09311 9 $172,000 $199,90012 10 $180,000 $215,89213 11 $188,000 $233,16414 12 $196,000 $251,81715 13 $204,000 $271,96216 14 $212,000 $293,71917 15 $220,000 $317,21718 16 $228,000 $342,59419 17 $236,000 $370,00220 18 $244,000 $399,60221 19 $252,000 $431,57022 20 $260,000 $466,09623 21 $268,000 $503,38324 22 $276,000 $543,65425 23 $284,000 $587,14626 24 $292,000 $634,11827 25 $300,000 $684,848

Now create a single scatter graph where future value is on the y-axis and time is on the x-axis. Plot the values for both accounts on the same graph.

To draw a graph, you may either click on the chart wizard button

or use “Insert Chart” from the menu.

Question 1

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B C D E F G2 Present Value = $100,000 Year Simple Compound3 Interest Rate = 8% 1 $108,000 $108,0004 2 $116,000 $116,6405 3 $124,000 $125,9716 4 $132,000 $136,0497 5 $140,000 $146,9338 6 $148,000 $158,6879 7 $156,000 $171,382

10 8 $164,000 $185,09311 9 $172,000 $199,90012 10 $180,000 $215,89213 11 $188,000 $233,16414 12 $196,000 $251,81715 13 $204,000 $271,96216 14 $212,000 $293,71917 15 $220,000 $317,21718 16 $228,000 $342,59419 17 $236,000 $370,00220 18 $244,000 $399,60221 19 $252,000 $431,57022 20 $260,000 $466,09623 21 $268,000 $503,38324 22 $276,000 $543,65425 23 $284,000 $587,14626 24 $292,000 $634,11827 25 $300,000 $684,848

Add trendlines to each graph.

To add a trendline:1. Place mouse over any data point of

the desired function.2. Right-click the mouse.3. Select “Add Trendline”.4. Choose the function that resembles

the pattern

Question 1

$0

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$700,000

$800,000

0 5 10 15 20 25

Years

Fu

ture

Val

ue

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B C D E F G2 Present Value = $100,000 Year Simple Compound3 Interest Rate = 8% 1 $108,000 $108,0004 2 $116,000 $116,6405 3 $124,000 $125,9716 4 $132,000 $136,0497 5 $140,000 $146,9338 6 $148,000 $158,6879 7 $156,000 $171,382

10 8 $164,000 $185,09311 9 $172,000 $199,90012 10 $180,000 $215,89213 11 $188,000 $233,16414 12 $196,000 $251,81715 13 $204,000 $271,96216 14 $212,000 $293,71917 15 $220,000 $317,21718 16 $228,000 $342,59419 17 $236,000 $370,00220 18 $244,000 $399,60221 19 $252,000 $431,57022 20 $260,000 $466,09623 21 $268,000 $503,38324 22 $276,000 $543,65425 23 $284,000 $587,14626 24 $292,000 $634,11827 25 $300,000 $684,848

The difference between them is almost $400,000.

The difference between them is exactly $384,848.

Question 1

$0

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$700,000

$800,000

0 5 10 15 20 25

Years

Fu

ture

Val

ue

10

$0

$200,000

$400,000

$600,000

$800,000

$1,000,000

$1,200,000

$1,400,000

$1,600,000

$1,800,000

0 5 10 15 20 25

Years

Fu

ture

Val

ue

Question 2

B C D E F G2 Present Value = 100000 Year Simple Compound3 Interest Rate = 12% 1 $112,000 $112,0004 2 $124,000 $125,4405 3 $136,000 $140,4936 4 $148,000 $157,3527 5 $160,000 $176,2348 6 $172,000 $197,3829 7 $184,000 $221,068

10 8 $196,000 $247,59611 9 $208,000 $277,30812 10 $220,000 $310,58513 11 $232,000 $347,85514 12 $244,000 $389,59815 13 $256,000 $436,34916 14 $268,000 $488,71117 15 $280,000 $547,35718 16 $292,000 $613,03919 17 $304,000 $686,60420 18 $316,000 $768,99721 19 $328,000 $861,27622 20 $340,000 $964,62923 21 $352,000 $1,080,38524 22 $364,000 $1,210,03125 23 $376,000 $1,355,23526 24 $388,000 $1,517,86327 25 $400,000 $1,700,006

What is the difference in results between savings accounts that use simple and

compound interest when you invest $100,000 at 12% for 25 years?

Note the change of scale on the y-axis

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$0

$50,000

$100,000

$150,000

$200,000

$250,000

0 5 10 15 20 25

Years

Fu

ture

Val

ue

Question 3

B C D E F G2 Present Value = 100000 Year Simple Compound3 Interest Rate = 3% 1 $103,000 $103,0004 2 $106,000 $106,0905 3 $109,000 $109,2736 4 $112,000 $112,5517 5 $115,000 $115,9278 6 $118,000 $119,4059 7 $121,000 $122,987

10 8 $124,000 $126,67711 9 $127,000 $130,47712 10 $130,000 $134,39213 11 $133,000 $138,42314 12 $136,000 $142,57615 13 $139,000 $146,85316 14 $142,000 $151,25917 15 $145,000 $155,79718 16 $148,000 $160,47119 17 $151,000 $165,28520 18 $154,000 $170,24321 19 $157,000 $175,35122 20 $160,000 $180,61123 21 $163,000 $186,02924 22 $166,000 $191,61025 23 $169,000 $197,35926 24 $172,000 $203,27927 25 $175,000 $209,378

What is the difference in results between savings accounts that use simple and

compound interest when you invest $100,000 at 3% for 25 years?

Note the change of scale on the y-axis

12

$0

$2,000,000

$4,000,000

$6,000,000

$8,000,000

$10,000,000

$12,000,000

0 5 10 15 20 25

Years

Fu

ture

Val

ue

Question 4

What is the difference in results between savings accounts that use simple and

compound interest when you invest $100,000 at 20% for 25 years?

B C D E F G2 Present Value = 100000 Year Simple Compound3 Interest Rate = 20% 1 $120,000 $120,0004 2 $140,000 $144,0005 3 $160,000 $172,8006 4 $180,000 $207,3607 5 $200,000 $248,8328 6 $220,000 $298,5989 7 $240,000 $358,31810 8 $260,000 $429,98211 9 $280,000 $515,97812 10 $300,000 $619,17413 11 $320,000 $743,00814 12 $340,000 $891,61015 13 $360,000 $1,069,93216 14 $380,000 $1,283,91817 15 $400,000 $1,540,70218 16 $420,000 $1,848,84319 17 $440,000 $2,218,61120 18 $460,000 $2,662,33321 19 $480,000 $3,194,80022 20 $500,000 $3,833,76023 21 $520,000 $4,600,51224 22 $540,000 $5,520,61425 23 $560,000 $6,624,73726 24 $580,000 $7,949,68527 25 $600,000 $9,539,622

$0

$2,000,000

$4,000,000

$6,000,000

$8,000,000

$10,000,000

$12,000,000

0 5 10 15 20 25

Years

Fu

ture

Val

ue

Note the change of scale on the y-axis

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Assignment

1. Expand the number of years on your spreadsheet to 50 and redo the graph to include the new values. Does the compound interest graph for an interest rate of 3% still look linear? (Refer to Slide 11 for comparison.)

2. How long does it take for $10,000 to double at 5% using simple interest?

3. How long does it take for $10,000 to double at 5% using compound interest? (round answer to nearest year)

4. Redo questions #2 and #3 using interest rates of 10%, 15%, and 20%?

5. Redo questions #2 through #4 using $2585. Did it make a difference in the amount of time for each to double, and if so, longer or shorter?

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Assignment

6. Compute the future value using simple interest if you deposit $5,000 for 20 years at 12%.

7. Compute the future value using compound interest if you deposit $5,000 for 20 years at 6.5%.

8. How do the results from questions #6 and #7 compare?

9. Savings Accounts, Certificates of Deposit (CDs), New Car Loans, Credit Cards, and Mortgages – which of these use simple and which use compound interest?

10. Based on your answer to question #9, which interest method is used most and why do you think that is the case?