Fix bug 4675

Author: gajennings

OpenProblemLibrary/NAU/setActuarial/setExamFM10.pg

@@ -5,6 +5,7 @@
 ## Institution(NAU)
 ## Author(Michael Ratliff)
 ## Level(4)
+## MO(1)
 ## KEYWORDS('force of interest')
 ##ENDDESCRIPTION
 
@@ -14,29 +15,49 @@ DOCUMENT();
 
 loadMacros(
   "PGstandard.pl",
-  "PGchoicemacros.pl",
+  "MathObjects.pl",
   "PGasu.pl",
   "PGcourse.pl"
 );
 
-TEXT(&beginproblem);
+TEXT(beginproblem());
+
+Context("Numeric");
 
 $a = random(2,5,1);
 $b = $a + random(1,3,1);
 
-$pre = 1000*(2.71828**((2*$a+$b)/100));
-$ans=round(100*$pre)/100;
+# Let V(t)=value of investment at time t, where t is 
+# measured in years from Jan. 1, 2004.  The force of interest is
+# delta_t = ($a + $b*t)/50 = (d/dt)ln(V(t))
+# so ln(V(t))-ln(V(t0)) = $a*(t-t0)/50 + $b*(t^2-t0^2)/100 and
+# V(t)/V(t0) = exp( $a*(t-t0)/50 + $b*(t^2-t0^2)/100 )
+# 2004 is a leap year: Jan. 1 - June 30 is 181 days out of 366
+# so t0 = 181/366 on July 1, 2004 and t = 1 on Jan. 1 2005
+# V(t0) = 1000 so the answer is 
+# V(1)=1000*exp($a*(1-t0)/50 + $b*(1^2-t0^2)/100 )  
+
+$t0 = 181/366;
+$V = 1000*exp( $a*(1-$t0)/50 + $b*(1**2-$t0**2)/100 ) ;
+
+# round answer to nearest cent
 
+$ans = Real( round(100*$V)/100 ); 
 
 
-TEXT(EV2(<<EOT));
+#$pre = 1000*(2.71828**((2*$a+$b)/100));
+#$ans=round(100*$pre)/100;
 
-On July 1, 2004, a person invested $DOLLAR 1,000 in a fund for which the force of interest at time \(t\) is given by \( \delta_t = \frac{$a + $b t}{50}\), where \(t\) is the number of years since January 1, 2004.  Determine the accumulated value of the investment on January 1, 2005.
+
+Context()->texStrings;
+BEGIN_TEXT
+
+On July 1, 2004, a person invested ${DOLLAR}1,000 in a fund for which the force of interest at time \(t\) is given by \( \delta_t = \frac{$a + $b t}{50}\), where \(t\) is the number of years since January 1, 2004.  Determine the accumulated value of the investment on January 1, 2005.
 
 $BR
 Accumulated value of the investment = $DOLLAR \{ans_rule(20)\}
-EOT
-
-&ANS(num_cmp($ans));
+END_TEXT
+Context()->normalStrings;
 
+ANS($ans->cmp(tolerance=>2, tolType=>'absolute'));
 ENDDOCUMENT();