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Compound Interest Tables (Excerpt from Table 6.1)

# Compound Interest Tables (Excerpt from Table 6.1)

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Compound Interest Tables

Formula for future value factor (FVF) for 1

FVFn ,i = ( 1 + i )

n

Where:

FVFn,i = future value factor for n periods at i interest

n = number of periods

i = rate of interest for a single period

LO 1

18

Compound Interest Tables

Frequency of Compounding

Determine number of periods by multiplying number of years involved by number of compounding periods

per year.

12% Annual Interest Rate over 5 Years

Interest Rate per Compounding Period

Number of Compounding Periods

Compounded

Annually (1)

.12 ÷ 1 = .12

Semiannually (2)

.12 ÷ 2 = .06

Quarterly (4)

.12 ÷ 4 = .03

Monthly (12)

.12 ữ 12 = .01

LO 1

Copyright â2019 John Wiley & Sons, Inc.

5 years × 1 compounding per year = 5 periods

5 years × 2 compoundings per year = 10 periods

5 years × 4 compoundings per year = 20 periods

5 years × 12 compoundings per year = 60 periods

19

Compound Interest Tables

Comparison of Different Compounding Periods

A 9% annual interest compounded daily provides a 9.42% yield.

Effective Yield for a \$10,000 investment.

LO 1

Copyright â2019 John Wiley & Sons, Inc.

20

Fundamental Variables

LO 1

Rate of Interest

Number of Time Periods

Future Value

Present Value

Copyright â2019 John Wiley & Sons, Inc.

21

Learning Objective 2

Solve Future and Present Value of 1 Problems

LO 2

22

Single-Sum Problems

Two Categories

Unknown Present Value

LO 2

Unknown Future Value

23

Future Value of a Single Sum

Value at a future date of a given amount invested, assuming compound interest.

(

FV = PV FVFn ,i

)

Where:

FV = future value

PV = present value (principal or single sum)

FVFn, i = future value factor for n periods at i interest

LO 2

24

Future Value of a Single Sum

Illustration

Bruegger Co. wants to determine the future value of \$50,000 invested for 5 years compounded annually at

an interest rate of 6%.

Future value = PV( FVFn,i )

= \$50, 000(FVF5,6% )

= \$50, 000(1+ .06)5

= \$50, 000(1.33823)

= \$66, 912

LO 2

25

Future Value of a Single Sum

Alternate Calculation

Bruegger Co. wants to determine the future value of \$50,000 invested for 5 years compounded annually at

an interest rate of 6%.

What table do we use?

LO 2

26

Future Value of a Single Sum

Alternate Calculation with Table

TABLE 6.1 FUTURE VALUE OF 1 (FUTURE VALUE OF A SINGLE SUM)

i=6%

n=5

What factor do we use?

\$50,000

Present Value

LO 2

x

1.33823

=

Factor

\$66,912

Future Value

27

Future Value of a Single Sum

Illustration

Assume that Commonwealth Edison Company deposited \$250 million in an escrow account with Northern Trust

Company at the beginning of 2020 toward a power plant to be completed December 31, 2023. How much will the

company have on deposit at the end of 4 years if interest is 10%, compounded semiannually?

Present Value

Future Value

\$250,000,000

What table do we use?

LO 2

28

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Compound Interest Tables (Excerpt from Table 6.1)

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