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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 \$b = random(1000,2000,100);
35 \$t = random(11,20,1);
36 \$ip = random(7.0,9.7,0.1);
37 \$i = \$ip*0.01;
38
39 TEXT(EV2(<<EOT));
40
41 Little Suzie wins \$a dollars in the Extreme Pit-Fighting Championship,
42 and immediately deposits the prize money in a savings account paying a
43 nominal interest rate of \$ip percent convertible monthly. Five months later, she
44 withdraws \$b dollars from the account.
45 How much money is in the account \$t months after the initial deposit?
46 (Assume no other deposits or withdrawals were made to the account.)
47
48
49 \$BR
50 \$PAR
51 Answer =  \{ans_rule(35) \} dollars.
52 \$BR
53 \$BR
54
55 EOT
56
57 \$ans = \$a*(1+\$i/12)**\$t - \$b*(1+\$i/12)**(\$t-5);
58 ANS(num_cmp(\$ans));
59
60 ENDDOCUMENT();
```