<div id="app">
  <div class="checkbox-item">
    <input type="checkbox" name="" id="c1" value="16000" class="checkbox" v-model="inputs">
    <label for="c1">Пакет 1</label>
  </div>
  <div class="checkbox-item">
    <input type="checkbox" name="" id="c2" value="17000" class="checkbox" v-model="inputs">
    <label for="c2">Пакет 2</label>
  </div>
  <div>
    {{summ}}
  </div>
</div>

let app = new Vue({
  el: "#app",
  data: {
    inputs: []
  },
  methods: {},
  computed: {
    summ() {
      return this.inputs.reduce((sum, value) => sum + parseInt(value), 0);
    }
  }
});