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=?

7

8

$-

$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

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

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

12

$-

$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

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

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

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

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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