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```    1 ## DESCRIPTION
2 ##  Financial mathematics: Effective and nominal rates of interest
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('financial mathematics', 'effective and nominal rates')
6 ## JJH tagged this problem.
7
8 ## DBsubject('Financial Mathematics')
9 ## DBchapter('Introduction to Interest')
10 ## DBsection('Effective and Nominal Rates of Interest')
11 ## Date('5/22/2005')
12 ## Author('Jeff Holt')
13 ## Institution('UVA')
14 ## TitleText1('Financial Mathematics')
15 ## EditionText1('1')
16 ## AuthorText1('Holt')
17 ## Section1('1.3')
18 ## Problem1()
19
20 DOCUMENT();
21
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.pl",
27 "PGauxiliaryFunctions.pl"
28 );
29
30 TEXT(beginproblem());
32
33 \$a = random(6000,8000,100);
34 \$ip = random(5.0,9.7,0.1);
35 \$i = \$ip*0.01;
36
37 TEXT(EV2(<<EOT));
38
39 An investment pays \$ip percent nominal interest convertible
40 semiannually.  What is the equivalent nominal rate of interest convertible
41 monthly?
42
43 \$BR
44 \$PAR
45 Answer =  \{ans_rule(35) \} percent.
46 \$BR
47 \$BR
48
49 EOT
50
51 \$ans = 100*((1 + \$i/2)**(1/6) - 1)*12;
52 ANS(num_cmp(\$ans, format => '%0.3f', tol => .001));
53
54 ENDDOCUMENT();
```