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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



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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



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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



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Fundamental Variables



LO 1







Rate of Interest







Number of Time Periods







Future Value







Present Value



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21



Learning Objective 2

Solve Future and Present Value of 1 Problems



LO 2



Copyright ©2019 John Wiley & Sons, Inc.



22



Single-Sum Problems

Two Categories



Unknown Present Value



LO 2



Unknown Future Value



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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



Copyright ©2019 John Wiley & Sons, Inc.



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



Copyright ©2019 John Wiley & Sons, Inc.



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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



Copyright ©2019 John Wiley & Sons, Inc.



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



Copyright ©2019 John Wiley & Sons, Inc.



$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



Copyright ©2019 John Wiley & Sons, Inc.



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Compound Interest Tables (Excerpt from Table 6.1)

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