Added the following functions to SubBooking:

Query scopes:
    interval($start, $end)
    joinBookings()
    withSignedAmount()
    joinAccountBranch()
  Sum functions:
    balanceAt($date)
    expedituresInInterval($start, $end, $group)
    incomesInInterval($start, $end, $group)
    cashFlowInInterval($start, $end, $type, $group)

app/SubBooking.php

@@ -3,6 +3,8 @@
 namespace App;
 
 use Illuminate\Database\Eloquent\Model;
+use Illuminate\Support\Facades\DB;
+use Carbon\Carbon;
 
 class SubBooking extends Model
 {
@@ -11,6 +13,189 @@ class SubBooking extends Model
         return $this->ioType->factor * $this->amount;
     }
 
+    /**************************************************************************
+     * SUMS OVER INCOMES AND EXPEDITURES, ACCOUNT BALANCES                    *
+     **************************************************************************/
+
+    /**
+     * Return the balance at a given date.
+     * 
+     * @param  string $date
+     * @return float 
+     */
+    public static function balanceAt($date)
+    {
+        $date = Carbon::parse($date)->format('Y-m-d');
+
+        $result = SubBooking::joinAccountBranch()
+                            ->joinBookings()
+                            ->where('bookings.date', '<=', $date)
+                            ->selectRaw('sum(i_o_types.factor * sub_bookings.amount) as balance')
+                            ->first()->balance;
+
+        return is_null($result) ? 0.00 : $result;
+    }
+
+    /**
+     * Return the sum of all expeditures in the given interval.
+     *
+     * Return the sum of all expeditures in the interval from $star to $end.
+     * If $group is true, the result is grouped by year and month, such that the
+     * collection contains for every month in the interval an model with the
+     * properties 'year', 'month' and 'expeditures'.
+     * Otherwise the result is a collection with a single model, containing the
+     * property 'expeditures'.
+     *
+     * @param  string  $start
+     * @param  string  $end
+     * @param  string $group Toggle, if the result is grouped by year and month.
+     * @return Illuminate\Database\Eloquent\Collection
+     */
+    public static function expedituresInInterval($start, $end, $group = false)
+    {
+        return SubBooking::cashFlowInInterval($start, $end, 'expeditures', $group);
+    }
+    
+    /**
+     * Return the sum of all expeditures in the given interval.
+     *
+     * Return the sum of all expeditures in the interval from $star to $end.
+     * If $group is true, the result is grouped by year and month, such that the
+     * collection contains for every month in the interval an model with the
+     * properties 'year', 'month' and 'incomes'.
+     * Otherwise the result is a collection with a single model, containing the
+     * property 'incomes'.
+     *
+     * @param  string  $start
+     * @param  string  $end
+     * @param  string $group Toggle, if the result is grouped by year and month.
+     * @return Illuminate\Database\Eloquent\Collection
+     */
+    public static function incomesInInterval($start, $end, $group = false)
+    {
+        return SubBooking::cashFlowInInterval($start, $end, 'incomes', $group);
+    }
+
+    /**
+     * Since the incomesInInterval and expedituresInInterval methods are almost
+     * the same, this is the collectively used code.
+     *
+     * @param  string $start
+     * @param  string $end
+     * @param  string $type  Can be 'incomes' or 'expeditures'
+     * @param  string $group Toggle, if the result is grouped by year and month.
+     * @return Illuminate\Database\Eloquent\collection
+     */
+    private static function cashFlowInInterval($start, $end, $type, $group = false)
+    {
+        $parsedStart = Carbon::parse($start);
+        $parsedEnd = Carbon::parse($end);
+
+        $typeName = ($type === 'incomes') ? 'Einnahme' : 'Ausgabe';
+
+        $start = $parsedStart->format('Y-m-d');
+        $end = $parsedEnd->format('Y-m-d');
+
+        $result = SubBooking::joinAccountBranch()
+                            ->interval($start, $end)
+                            ->where('i_o_types.name', '=', $typeName)
+                            ->selectRaw('sum(i_o_types.factor * sub_bookings.amount) as ' . $type);
+
+        if ($group) {
+            // Group the result, first by month, then by year
+            $result = $result->groupBy('year', 'month')
+                             ->selectRaw('sum(i_o_types.factor * sub_bookings.amount) as ' . $type . ',
+                                YEAR(bookings.date) as year,
+                                MONTH(bookings.date) as month')
+                             ->get();
+
+            // Add a model with values = 0 for those months without any
+            // sub-booking. If we would not explicitly define a model for these
+            // cases, we would try toget a property from a model that does not
+            // exist. 
+            $yearStart = $parsedStart->format('Y');
+            $yearEnd = $parsedEnd->format('Y');
+
+            for ($year = $yearStart; $year <= $yearEnd; $year++) {
+                // Set the start and end month for a year, in case the given
+                // interval starts or ends in the current year.
+                $monthStart = ($year == $parsedStart->format('Y')) ?
+                              $parsedStart->format('n') :
+                              1;
+                $monthEnd = ($year == $parsedEnd->format('Y')) ?
+                             $parsedEnd->format('n') :
+                             12;
+
+                for ($month = $monthStart; $month <= $monthEnd; $month++) {
+                    if ($result->where('year', '=', $year)
+                               ->where('month', '=', $month)->isEmpty()) {
+                        $subBooking = new SubBooking();
+
+                        $subBooking->$type = 0;
+                        $subBooking->year = (int) $year;
+                        $subBooking->month = (int) $month;
+
+                        $result->push($subBooking);
+                    }
+                }
+            }
+
+            return $result;
+        }
+
+        return $result->get();
+    }
+
+    /**************************************************************************
+     * QUERY SCOPES                                                           *
+     **************************************************************************/
+    
+    /**
+     * Consider only sub-bookings in a given interval.
+     *
+     * @return Illuminate\Database\Eloquent\Builder
+     */
+    public function scopeInterval($query, $start, $end)
+    {
+        return $query->joinBookings()
+                     ->where('bookings.date', '>=', Carbon::parse($start)->format('Y-m-d'))
+                     ->where('bookings.date', '<=', Carbon::parse($end)->format('Y-m-d'));
+    }
+
+    /**
+     * Join the 'bookings' table into the query.
+     *
+     * @return Illuminate\Database\Eloquent\Builder
+     */
+    public function scopeJoinBookings($query)
+    {
+        return $query->join('bookings', 'bookings.id', '=', 'sub_bookings.booking_id');
+    }
+
+    /**
+     * Add a signed amount property to the table.
+     *
+     * @return Illuminate\Database\Eloquent\Builder
+     */ 
+    public function scopeWithSignedAmount($query)
+    {
+        return $query->joinAccountBranch()
+                     ->addSelect(DB::raw('sub_bookings.*, (i_o_types.factor * sub_bookings.amount) as signedAmount'));
+    }
+
+    /**
+     * Join the tables 'i_o_types', 'account_classes' and 'account_types' into
+     * the query.
+     *
+     * @return Illuminate\Database\Eloquent\Builder
+     */
+    public function scopeJoinAccountBranch($query)
+    {
+        return $query->join('account_types', 'account_types.id', '=', 'sub_bookings.account_type_id')
+                     ->join('account_classes', 'account_classes.id', '=', 'account_types.account_class_id')
+                     ->join('i_o_types', 'i_o_types.id', '=', 'account_classes.io_type_id');
+    }
+
     /**************************************************************************
      * BOOKINGS                                                               *
      **************************************************************************/