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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 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl"
   28 );
   29 
   30 TEXT(beginproblem());
   31 $showPartialCorrectAnswers = 1;
   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();