## Created by Nikola Kuzmanovski

########################################################################

DOCUMENT();      

loadMacros(
   "PGstandard.pl",
   "MathObjects.pl",
   "parserMultiAnswer.pl",
);

# Print problem number and point value (weight) for the problem
TEXT(beginproblem());

# Show which answers are correct and which ones are incorrect
$showPartialCorrectAnswers = 1;

##############################################################
#
#  Setup
#
#
Context("Numeric");
Context()->variables->add(t => "Real");
Context()->flags->set(
  tolerance => 0.0001,
  tolType => "absolute",
);
Context()->strings->add(U=>{});
Context()->strings->add(F=>{});

#Random constants for problem.
$I = random(1000, 10000, 1);
$cont= random(1,4, 0.1);
$comp =  random(1,4, 0.13);

#Correct answers
$correctU = Formula("$I*e^(($cont/100)*t)");										#Depends on I and cont
$correctF = Formula("$I*(1+ ($comp/100)/4)^(4*t)");									#Depends on I and comp
$correctURate = Formula("e^($cont/100)-1");										#Depends on cont
$correctFRate = Formula("(1+($comp/100)/4)^4-1");									#Depends on comp
$correctChoice = "U";													#URate is better by default

#If FRate is better than F is the correct choice.
if ((exp(1))**($cont/100)-1 < (1+($comp/100)/4)**4-1){
	$correctChoice = "F";
}


#Multi answer checker with partial credit.
$multians = MultiAnswer($correctU, $correctF, $correctURate, $correctFRate, $correctChoice)->with(
  singleResult => 0,
  allowBlankAnswers => 1,
  checkTypes => 0,
  checker => sub {
	my ( $correct, $student, $self ) = @_;
	my ( $stuU, $stuF, $stuURate, $stuFRate, $stuChoice ) = @{$student};						#Get student input
	my ( $U, $F, $URate, $FRate, $choice ) = @{$correct};								#Get correct answers
      
	my @ret = (0.0, 0.0, 0.0, 0.0, 0.0);										#Points for each correct answer


	#See if the first formula is correct
	#If there is some issue with the student input we just move on.
	#An issue with the student input is anything that will throw an exception.
	#The eval block will handle any exceptions and not crash the answer checker.
	eval{
		#Get the student I and cont.
		#We define I by evaluation at 0. 
		#Definition of cont is more complicated, but same idea.
		my $stuInitialValU = $stuU->eval(t=>0);									#Student I
		my $stuUContRate = log(($stuU->eval(t=>1))/$stuInitialValU);						#Student cont
		
		#If student got I correct, we give them half the points. 
		if( $I == $stuInitialValU) {
			$ret[0] = $ret[0] + 0.5;
		}
		
		#If student got cont correct we give them the rest of the points.
		if ( $cont/100 == $stuUContRate) {
			$ret[0] = $ret[0] +0.5;
		}
	} or do {
		#Find a way to show some error message to student that might be helpful
	};



	#See if the second formula is correct
	#If there is some issue with the student input we just move on.
	#An issue with the student input is anything that will throw an exception.
	#The eval block will handle any exceptions and not crash the answer checker.
	eval{
		#Get the student I and comp.
		#We define I by evaluation at 0. 
		#Definition of comp is more complicated, but same idea.
		my $stuInitialValF = $stuF->eval(t=>0);									#Student I
		my $stuFGrothFactor = ($stuF->eval(t=>1)/$stuInitialValF);						#Student comp growth factor

		#If student got I correct, we give them half the points. 
		if ( $I == $stuInitialValF ) {
			$ret[1] = $ret[1] + 0.5;
		}

		#If student got cont correct we give them the rest of the points.
		if ( (1+($comp/100)/4)**4 == $stuFGrothFactor ) {
			$ret[1] = $ret[1] +0.5;
		}
	} or do {
		#Find a way to show some error message to student that might be helpful
	};



	#Check if the effective rate for U bank is correct.
	#This answer depends on the formula U(t) the student gave
	#Effective annual reate is growth factor -1.
	#The growth factor is the base of t.
	eval{
		my $stuInitialValU = $stuU->eval(t=>0);									#Student I
		my $stuUContRate = log(($stuU->eval(t=>1))/$stuInitialValU);						#Student growth rate
	
		#Check if the student effective rate is correct based on their formula for U.
		if ( $stuURate == Compute("e^($stuUContRate) - 1")) {
			$ret[2] = 1;
		}
	} or do {
		#Find a way to show some error message to student that might be helpful
	};

	#Check if the effective rate for F bank is correct.
	#This answer depends on the formula F(t) the student gave
	#Effective annual reate is growth factor -1.
	#The growth factor is the base of t.
	eval{
		my $stuInitialValF = $stuF->eval(t=>0);									#Student I
		my $stuFGrothFactor = ($stuF->eval(t=>1)/$stuInitialValF);						#Student growth factor
	
		#Check if the student effective rate is correct based on their formula for F.
		if ( $stuFRate == Compute("$stuFGrothFactor -1")) {
			$ret[3] = 1;
		}
	} or do {
		#Find a way to show some error message to student that might be helpful
	};

	#Check if student made correct choice for a bank based on their input.
	if ( ($stuURate > 0 && $stuFRate > 0) && (
		($stuURate < $stuFRate && $stuChoice == "F") ||
		($stuURate > $stuFRate && $stuChoice == "U") )){
		$ret[4] = 1;
	}

	return [ @ret ];
	}
);


##############################################################
#
#  Text
#
#

Context()->texStrings;
BEGIN_TEXT


Loretta is trying to determine which bank she should open a savings account at. 
Loretta plans to make an initial deposit of $$I, and plans to use this money to make a down payment on a house sometime in the undisclosed future.
$BR

$BR
Union Bank offers an account with a nominal annual rate of $cont%, compounded continuously.
$BR

First National Bank offers an account with a nominal annual rate of $comp%, compounded quarterly.
$BR
$BR

a) Write down the function that gives the amount of money Loretta will have in t years if she uses the Union Bank account.
$BR
\(U(t) = \) \{ans_rule(50)\}.
$BR
$BR

b) Write down the function that gives the amount of money Loretta will have in t years if she uses the First National Bank account.
$BR
\(F(t) = \) \{ans_rule(50)\}.
$BR
$BR

c) Compute the effective annual rate of both banks.
$BR

Effective annual rate for Union Bank: \{ans_rule(50)\}%.
$BR
Effective annual rate for First National Bank: \{ans_rule(50)\}%.

Which Bank will make Loretta more money? 
Enter U for Union bank.
Enter F for First National Bank.
$BR
\{ans_rule(1)\}

END_TEXT
Context()->normalStrings;

##############################################################
#
#  Answers
#
#


ANS($multians->cmp());

ENDDOCUMENT();