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TRANSCRIPT
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This project has been supported by an American Council on Education – Alfred P. Sloan Foundation Faculty Retirement Transition award to San José State University
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Financial Literacy Module 1 – Time Value of Money (TVM) and the Power of Compounding
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Overview
Time Value Of Money (TVM) ◦ Definition ◦ Why Do We Care? ◦ Examples ◦ Graphs
Conclusion
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The Power of Compounding
“A nearby penny is worth a distant dollar”, Anonymous
“The most powerful force in the universe is compound interest”, Albert Einstein
“…the world’s greatest invention was 6 per cent compound interest, which goes on twenty-four hours a day, seven days a week and fifty-two weeks a year.”, Roger W. Babson
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TVM - Compounding $1 invested today at r% per year for n
years 0 1 2 3 n
$1 ? r %
nn rCFV )1( +×=
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TVM – Compounding – Single Cash Flow - Example 1 $1,000 invested today at 8% per year for
10 years 0 1 2 3 10
$1,000 FV=? 8%
92.158,2$)08.1(000,1$ 1010 =×=FV
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TVM – Compounding – Single Cash Flow - Example 2 $1,000 invested today at 8% per year for
30 years 0 1 2 3 30
8%
66.062,10$)08.1(000,1$ 3030 =×=FV
$1,000 FV=?
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$-
$2,000.00
$4,000.00
$6,000.00
$8,000.00
$10,000.00
$12,000.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
$1,000 invested at 8% for 30 years
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TVM – Compounding – Single Cash Flow - Example 3 $1,000 invested today at 10% per year for
30 years 0 1 2 3 30
10%
40.449,17$)1.1(000,1$ 3030 =×=FV
$1,000 FV=?
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TVM – Compounding – Ordinary Annuity - Example 1 Series of cash flows: $300 invested at the end of each
month for 10 years at 8% per year (APR)
0 1 2 3 120
8%
( ) ( )
%6667.012%812
81.883,54$006667.0
1006667.1300$11
11 120
120
====
=
−×=
−
+
×=
−+×=
×
×
iratemonthlyim
mr
mr
Ci
iCFV
mn
mn
$300
FV=?
10
$300 $300 $300
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TVM – Compounding – Ordinary Annuity - Example 2 Series of cash flows: $300 invested at the end of each
month for 30 years at 8% per year (APR)
0 1 2 3 360
8%
( ) ( )
%6667.012%812
83.107,447$006667.0
1006667.1300$11
11 360
360
====
=
−×=
−
+
×=
−+×=
×
×
iratemonthlyim
mr
mr
Ci
iCFV
mn
mn
$300
FV=?
11
$300 $300 $300
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$-
$100,000
$200,000
$300,000
$400,000
$500,000
$600,000
1 9 17 25 33 41 49 57 65 73 81 89 97 105
113
121
129
137
145
153
161
169
177
185
193
201
209
217
225
233
241
249
257
265
273
281
289
297
305
313
321
329
337
345
353
$300 Monthly Ordinary Annuity Invested at 8% p.a. for 30 Years
Total Amount Invested - No Interest Future Value of $300 Ordinary Annuity with Interest
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TVM – Compounding – Ordinary Annuity - Example 3
Series of cash flows: …..similar to example 2, but NO contributions during years 6-10.
0 1 2 3 360
8%
( ) ( ) ( )
338,506.02$
006667.01006667.1300$006667.1
006667.01006667.1300$
240300
60
360
=
−×+
×
−×=FV
$300
FV=?
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$300 $300 $300
60
$300
61
$0
120
$0
121
$300
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TVM – Compounding – Ordinary Growing Annuity - Example 1 Series of cash flows: monthly investment of $300 and
growing 3% per year (APR) invested for 30 years at 8% per year (APR)
0 1 2 3 360
8%
( ) ( ) ( ) ( )
%25.012%3%6667.0
12%8
610,480$0025.0006667.00025.1006667.1300$11 360360
360
====
=
−−
×=
−+−+
×=××
gi
gigiCFV
mnmn
$300
FV=?
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$300.75 $301.50 $737.05
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TVM – The Pernicious Effect of Inflation The purchasing power of a monthly income of $2,000
over a twenty-year period when the annual inflation rate is 3% (APR)
0 1 2 240
$2,000
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$2,000 $2,000 $2,000
$2,000 $1,995.01 $1,990.04 $1,098.45
Purchasing Power
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Conclusion
TVM and the Power of Compounding can be Your Friends
When is it Best to Start Saving?
How do I Save?
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This project has been supported by an American Council on Education – Alfred P. Sloan Foundation Faculty Retirement Transition award to San José State University
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