Prosent - Dømi

Innleiðing

Í hesum trimum filmunum rokna vit við frymlunum \(S = B(1+r)\) og \(r = \frac{S}{B} - 1\) og \(B = \frac{S}{1+r}\). Hvør filmur loysir fyri hvørt av teimum trimum virðunum.

Byrja við at hyggja at filmunum, og royn síðan samvirkna dømi niðanfyri.

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Filmur 1 - Rokna \(S\)

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Filmur 2 - Rokna \(B\)

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Filmur 3 - Rokna \(r\)

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Samvirkið dømi: \(S\), \(B\) og \(r\)

Vel hvørji virði tú vilt rokna, set tølini inn, og síggj úrslitið.

{
  // Inputs (Observable Inputs handle their own rendering and events)
  const solveInp = Inputs.radio(["S", "B", "r"], {
    label: "Rokna fyri",
    value: "S",
    format: v => ({"S": "S - endavirði", "B": "B - byrjanarvirði", "r": "r - vakstrartal"})[v]
  });
  const BInp = Inputs.number({ label: "B - byrjanarvirði", value: 1000, step: 1 });
  const rInp = Inputs.number({ label: "r - vakstrartal (%)", value: 8, step: 0.1 });
  const SInp = Inputs.number({ label: "S - endavirði", value: 1080, step: 1 });

  // Result display box
  const resBox = document.createElement("div");
  resBox.style.cssText = "margin-top:1rem;padding:1rem 1.2rem;border-radius:6px;"
    + "border:1px solid var(--bs-border-color,#9ec5fe);"
    + "background:var(--bs-primary-bg-subtle,#e7f1ff);";

  const resFormula = document.createElement("div");
  resFormula.style.cssText = "font-size:0.9rem;color:var(--bs-secondary-color,#6c757d);margin-bottom:0.4rem;";

  const resAnswer = document.createElement("div");
  resAnswer.style.cssText = "font-size:1.7rem;font-weight:700;color:var(--bs-primary,#0d6efd);";

  resBox.appendChild(resFormula);
  resBox.appendChild(resAnswer);

  function fmt(n) {
    if (!isFinite(n)) return "?";
    const a = Math.abs(n);
    const d = a === 0 ? 0 : a < 0.01 ? 6 : a < 1 ? 4 : a < 100 ? 2 : 1;
    return parseFloat(n.toFixed(d)).toString().replace(".", ",");
  }

  function update() {
    const solve = solveInp.value;
    const B = BInp.value ?? 0;
    const r = (rInp.value ?? 0) / 100;
    const S = SInp.value ?? 0;

    if (solve === "S") {
      const v = B * (1 + r);
      resFormula.textContent = `S = B · (1 + r) = ${fmt(B)} · (1 + ${fmt(r)})`;
      resAnswer.textContent  = `S = ${fmt(v)}`;
    } else if (solve === "B") {
      const v = (1 + r) !== 0 ? S / (1 + r) : NaN;
      resFormula.textContent = `B = S / (1 + r) = ${fmt(S)} / (1 + ${fmt(r)})`;
      resAnswer.textContent  = `B = ${fmt(v)}`;
    } else {
      const v = B !== 0 ? S / B - 1 : NaN;
      resFormula.textContent = `r = S/B − 1 = ${fmt(S)} / ${fmt(B)} − 1`;
      resAnswer.textContent  = `r = ${fmt(v * 100)} %  (${fmt(v)})`;
    }
  }

  [solveInp, BInp, rInp, SInp].forEach(inp => inp.addEventListener("input", update));
  update();

  // Assemble
  const wrap = document.createElement("div");
  wrap.style.maxWidth = "420px";
  [solveInp, BInp, rInp, SInp, resBox].forEach(el => wrap.appendChild(el));
  return wrap;
}