Engineering Economic Analysis

----.------ _ d ~ontinuous Gompound~ng^115

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Compute an effectiveifor the time period between withdrawals.

Between withdrawals,W,there are four interest periods, hencem=4 compounding subperiods

per year. Since the nominal interest rate per year,r,is 8%, we can proceed to compute the effective

interest rate per year.

ffi

(

r

)

m

(

0.08

)

4'

E ectivemterestrate per year ia.= 1 + m - 1 = 1 + 4 - 1

=0.0824=8.24% per year

Now the problem may be redrawn as follows:

w w w w w

t t t t t

0-1-2-3-4-5

1

i=8.24% per year

n=5 years

$5000

This diagram may be directly solved to determine the annual withdrawalWusing tl),ecapital

recovery factor:

W=P(AI P, i, n)=5000(AI P,8.24%,5).

=P

[

i(1 +i)n

]

= 5000

[

0.0824(1 + 0.0824)5

(1 +i)n- 1 (1 + 0...0824)5- 1 ]

= 5000(0.2520) = $1260

The depositor should withdraw $1260 per year.

Continuous Compounding

Two variables we have introduced are:

r=Nominal interest rate per interest period

m=Number of compounding subperiods per time period

Since the interest period is normally one year, the definitions become:

r=Nominal interest rate per year

m=Number of compounding subperiods per year