28.08.2019 TIME WORTH OF MONEY SOLUTION SHEET

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TVM Formulation For:

1

Future Value of a

Huge. (FVIFi, n)

Compounded/Payments

(m) Times per Year

Annual Increasing

FVn sama dengan PV( one particular + i )n

two

FV

1 i

PHOTOVOLTAIC =

Present Value of the

Lump Sum. (PVIFi, n)

-n

Future Value of an

Annuity. (FVIFAi, n)

FVAn sama dengan CF

5

Present Benefit of an

Pension. (PVIFAi, n)

1 -- ( 1 + i actually )-n

PVAn = VOIR

i

a few

Present Value of

Perpetuity. (PVA )

6

Effective Annual Rate

given this.

7

The time

required for a PV to

grow to a FV.

eight

The APR required for

a PHOTOVOLTAIC to increase to a FV.

9

Present Value of

10

Present Value of

a Growing

Perpetuity.

11

The time

required for a series

of PMT's to expand to a

long term amount (FVAn).

12

EAR = APR

n=

(-m n)

m

-1

ln ( FV/PV)

m ln (1 i/m)

FV

PHOTOVOLTAIC

i= m

EAR = ei - 1

n=

ln (FV/PV)

i

i=

ln (FV/PV)

n

[1/(m n)]

-1

n

(FVA)(i)

+1

VOIR

ln (1 + i)

ln 1

n

n=

(1/n)

you g

1 i

(-i n)

CF0 1 g

i g

PVA

ln

i

EAR = you

m

-1

PV sama dengan FV electronic

CF

[(1 i/m) m 1]

PVA

i

CF0 1 g

1

i actually g

PVAn

1 -- 1 & i/m

PVAn = CF

i/m

ln (FV/PV)

ln (1 & i )

FV

i=

PV

(-m n)

( 1 + i/m )(m n) -- 1

i/m

FVAn = CF

VOIR

i

FV

(i n)

e

or

PV = FV 1 i/m

( 1 & i )n - one particular

i

three or more

n=

PV =

(m n)

(i n)

FVn = PHOTOVOLTAIC e

or

PV sama dengan FV( 1 + my spouse and i )

The length of time

required for a series

of PMT's to exhaust system a

specific present

quantity (PVAn).

FV

1 i/m

PV =

n

or perhaps

PVA

(m n)

FVn = PHOTOVOLTAIC 1 i/m

Continuous

Increasing

i

meters

ln

n=

(PVA)(i)

VOIR

,

ln (1 i)

meters

ln one particular

n

to get PVA(i) < CF

meters

FVA m

+

VOIR

i

ln (1 i/m)

(PVA)(i/m)

CF

,

ln(1 i/m)

for PVA(i/m) < VOIR

Legend

my spouse and i = APRIL, the nominal or Apr

m sama dengan the number of compounding periods per year

ln = the natural logarithm, the logarithm towards the base electronic

CF = PMT = the periodic payment or cash flow

in = the number of periods

EAR CANAL = the Effective Twelve-monthly Rate

electronic = the camp of the organic logarithm 2 . 71828вЂ¦

(Calculator: 1

ex )

Perpetuity = a great infinite pension

Prepared by Jim Keys