Annuities - E-Commerce - Lecture Slides, Slides of Fundamentals of E-Commerce

Students of Communication, study E-Commerce as an auxiliary subject. these are the key points discussed in these Lecture Slides of E-Commerce :Annuities, Future Value, Algebra, Ordinary Annuity, Periodic Cash, Interest Rate, Cash Flow, Earning, Interest Factor, Periodic Cash Flow

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2012/2013

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Annuities: Future Value – Algebra
Future value of an ordinary annuity
(
)
n
Ordinary
Annuity
1+i -1
FV = PMT
i
FV = future value of the annuity
PMT = equal periodic cash flow
i = the (annually compounded) interest rate
n = number of years
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pf3
pf4
pf5
pf8
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pfa

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Annuities: Future Value – Algebra • Future value of an

ordinary annuity (^ )

^

^

^

n 

OrdinaryAnnuity

1+i^ -

FV^

= PMT

i FV = future value of the annuityPMT = equal periodic cash flowi = the (annually compounded) interest raten = number of years

Annuities: Future Value

Example: What is the future value of a three yearordinary annuity with a cash flow of $100 peryear, earning 6%?

(^ ). ( ).

^

^

^

^

=^ 

^

^

n

OrdinaryAnnuity

1+i^ -1^3 FV^

= PMT

i^ 1 06^

Annuities: Future Value – Algebra Example: What is the future value of a threeyear annuity due with a cash flow of $100 peryear, earning 6%?

(^ )^

(^ )

(^ )

(^

.^

. .  $.

 ^

 ^

 ^

 ^

− =^ 

 ^

 ^

n

AnnuityDue

1+i^ -1^3 FV^

= PMT

1+i i 1 06^1 100

1 06 06 337 46

Annuities: Future Value – Table ● The future value of an ordinary annuity can becalculated using Table 4.3 (p. 145), where“future value of an ordinary annuity interestfactors” (FVIFA) are provided.

n^

i,n

FVAN

= PMT(FVIFA

), where:

+^ ( )

n − i,n

1 i^

1

FVIFA

=^

i

PMT = equal periodic cash flowi = the (annually compounded) interest raten = number of periodsFVAN = future value (ordinary annuity)FVIFA = future value interest factor

Annuity Due: Future Value ● Calculated using Table 4.3 (p. 145), whereFVIFAs are found. Ordinary annuity formula isadjusted to reflect one extra period of interest.

(^ )

^

 ^

+

n^

i,n

FVAND

= PMT FV

1 i IFA^

, where:

+^ ( )

n − i,n

1 i^

1

FVIFA

=^

i

PMT = equal periodic cash flowi = the (annually compounded) interest raten = number of periodsFVAND = future value (annuity due)FVIFA = future value interest factor

Annuity Due: Future Value Example:

What is the future value of a 3-year $100 annuity due if the cash flows are investedat 6% compounded annually?^ Table 4.3 Excerpt: FVIFA for $1 per period^ End of Period (n)

(^ )

^

+ ^

=^

= ^

 ^

n^

i,n

FVAND

= PMT FVIFA

1

i

$100 3.184(1.06)

$337.

Annuities: Present Value – Algebra^ ●^ Present value of an

ordinary annuity (^ )

^

^

^

-n 

OrdinaryAnnuity

1- 1+i

PV^

= PMT

i

PV = present value of the annuityPMT = equal periodic cash flowi = the (annually compounded) interest or discount raten = number of years