March 2014
Intermediate to advanced
412 pages
11h 16m
English
Content preview from Numerical Methods and Optimization
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92 Numerical Methods and Optimization: An Introduction
TABLE 4.1: Fixed point iterations for finding the interest rate with two
different choices for r
0
.
Iteration Approximate
number, k interest rate, r
k
0 r
0
=0.1 r
0
=0.2
1 0.112511 0.135264
2 0.116347 0.122372
3 0.117442 0.119091
4 0.117747 0.118203
5 0.117832 0.117958
6 0.117856 0.117891
7 0.117862 0.117872
8 0.117864 0.117867
9 0.117865 0.117865
10 0.117865 0.117865
We have p = 300,A=1, 000, 000, and n =12· 30 = 360, that is,
r =12
10
6
r
3600
+1
1/360
− 12 = f (r).
As a plausible initial approximation, we may take the value of r
0
=0.1.Then
the first approximation becomes
r
1
= f(r
0
)=f(0.1) = 0.112511.
Likewise, the sec
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