Engineering Economic Analysis

120 MORE INTERESTFORMULAS

(

er - 1

) (

eO.OO5- 1

A= F[AIF, r, n]= F ern_ 1 = 1000 eO.OO5(l2)_ 1)

= 1000

(

°.005013

)

= $81.07

0.061837

He would have to deposit $81.07 per month. Note that the differencebetween monthly and con-

tinuous compounding is just 3 cents per month.

Continuous, Uniform Cash Flow (One Period) with Continuous

Compounding at Nominal Interest Rate r

Equations for a continuous, uniform cash flow during one period only, with contin~ous

compounding, can be derived as follows. Let the continuous, uniform cash flow totalingP

be distributed overmsubperiods within one period (n=1). Thus PImis the cash flQw atthe

end of each subperiod. Since the nominal interest rate per period isr,the effective interest

rate per subperiod isrim. Substituting these values into the uniform series compound

amount equation (Equation 4-5) gives

F=p

[

[1 +(rlm)]m- 1

m rim ]

(4-45)

Settingx =rim,we obtain

F= P

[

[1+xY/x - 1

]

=P

[

[(1+X)l/xy -1

m rim r ]

(4-46)

Asmincreases,xapproaches zero. Equation 4-36 says

Xlim(1 +° X)l/x= e

hence Equation 4-46 for one period becomes

p

LJ' ,. ... .. ,

9

F .-

(4-47)

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