Calculating Weighted Average Life Formula

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Weighted Average Life Formula Calculator – Calculate Loan Repayment Period :root { –primary-color: #004a99; –success-color: #28a745; –background-color: #f8f9fa; –text-color: #333; –border-color: #ccc; –card-bg: #ffffff; –shadow: 0 2px 5px rgba(0,0,0,0.1); } body { font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif; background-color: var(–background-color); color: var(–text-color); line-height: 1.6; margin: 0; padding: 0; } .container { max-width: 1000px; margin: 20px auto; padding: 20px; background-color: var(–card-bg); border-radius: 8px; box-shadow: var(–shadow); } header { background-color: var(–primary-color); color: white; padding: 20px 0; text-align: center; border-radius: 8px 8px 0 0; margin-bottom: 20px; } header h1 { margin: 0; font-size: 2.2em; } h2, h3 { color: var(–primary-color); margin-top: 30px; margin-bottom: 15px; } .loan-calc-container { background-color: var(–card-bg); padding: 25px; border-radius: 8px; box-shadow: var(–shadow); margin-bottom: 30px; } .input-group { margin-bottom: 20px; display: flex; flex-direction: column; } .input-group label { display: block; margin-bottom: 8px; font-weight: bold; color: var(–primary-color); } .input-group input[type="number"], .input-group select { width: 100%; padding: 10px; border: 1px solid var(–border-color); border-radius: 4px; box-sizing: border-box; font-size: 1em; } .input-group .helper-text { font-size: 0.85em; color: #666; margin-top: 5px; } .error-message { color: red; font-size: 0.9em; margin-top: 5px; min-height: 1.2em; /* Reserve space */ } button { background-color: var(–primary-color); color: white; border: none; padding: 12px 20px; border-radius: 4px; cursor: pointer; font-size: 1.1em; margin-right: 10px; transition: background-color 0.3s ease; } button:hover { background-color: #003366; } button.secondary { background-color: #6c757d; } button.secondary:hover { background-color: #5a6268; } .results-container { margin-top: 30px; padding: 25px; background-color: var(–primary-color); color: white; border-radius: 8px; box-shadow: inset 0 2px 5px rgba(0,0,0,0.2); } .results-container h3 { color: white; margin-top: 0; margin-bottom: 15px; border-bottom: 1px solid rgba(255,255,255,0.3); padding-bottom: 10px; } .primary-result { font-size: 2.5em; font-weight: bold; text-align: center; margin-bottom: 20px; padding: 15px; background-color: var(–success-color); border-radius: 4px; } .intermediate-results div, .formula-explanation div { margin-bottom: 10px; font-size: 1.1em; } .intermediate-results span, .formula-explanation span { font-weight: bold; margin-right: 5px; display: inline-block; min-width: 150px; } .formula-explanation { margin-top: 20px; font-size: 0.95em; background-color: rgba(0, 0, 0, 0.05); padding: 15px; border-radius: 4px; } table { width: 100%; border-collapse: collapse; margin-top: 20px; margin-bottom: 30px; } th, td { padding: 12px; text-align: left; border-bottom: 1px solid var(–border-color); } th { background-color: var(–primary-color); color: white; font-weight: bold; } td { background-color: var(–card-bg); } caption { caption-side: top; font-weight: bold; color: var(–primary-color); margin-bottom: 10px; font-size: 1.1em; text-align: left; } canvas { display: block; margin: 20px auto; max-width: 100%; border: 1px solid var(–border-color); border-radius: 4px; } .article-section { margin-top: 40px; padding-top: 20px; border-top: 1px solid #eee; } .article-section h2 { text-align: center; font-size: 1.8em; margin-bottom: 25px; } .article-section h3 { font-size: 1.4em; margin-top: 30px; } .faq-item { margin-bottom: 20px; } .faq-item .question { font-weight: bold; color: var(–primary-color); cursor: pointer; display: block; margin-bottom: 5px; } .faq-item .answer { display: none; padding-left: 15px; border-left: 2px solid var(–primary-color); margin-top: 5px; } .internal-links ul { list-style: none; padding: 0; } .internal-links li { margin-bottom: 15px; } .internal-links a { color: var(–primary-color); text-decoration: none; font-weight: bold; } .internal-links a:hover { text-decoration: underline; } .internal-links p { font-size: 0.9em; color: #555; margin-top: 5px; } #copyButton { background-color: #ffc107; color: #212529; } #copyButton:hover { background-color: #e0a800; }

Weighted Average Life Formula Calculator

Understand the average time to repay your debt instrument.

Calculate Weighted Average Life (WAL)

The total amount of debt.
Total number of distinct payment periods.

Payment Schedule Details (Add up to 5 periods)

Amount paid in this period.
Time in years when this payment is made (e.g., 1 for end of year 1).
Amount paid in this period.
Time in years when this payment is made.
Amount paid in this period.
Time in years when this payment is made.
Amount paid in this period.
Time in years when this payment is made.
Amount paid in this period.
Time in years when this payment is made.

Calculation Results

—
Formula: WAL = Σ (Payment Amount * Time of Payment) / Total Principal
Total Principal: —
Weighted Sum of Payments: —
Total Payments Made: —

What is Weighted Average Life (WAL)?

The Weighted Average Life (WAL), also known as the average life of a debt security, is a measure used by investors and analysts to determine the average period of time over which the principal of a debt instrument is expected to be repaid. It takes into account the timing and amount of all scheduled principal payments, including amortization and any expected prepayments or balloon payments. Essentially, WAL provides a more nuanced view of repayment than simply looking at the final maturity date, especially for instruments with irregular payment schedules or features like sinking funds.

Who Should Use It:

  • Bond Investors: To assess the risk and expected return profile of corporate bonds, municipal bonds, and mortgage-backed securities. A shorter WAL might indicate lower interest rate risk.
  • Portfolio Managers: To manage the overall duration and cash flow characteristics of their fixed-income portfolios.
  • Underwriters and Issuers: To structure debt instruments and communicate repayment expectations to potential investors.
  • Financial Analysts: To compare different debt securities and make informed investment recommendations.

Common Misconceptions:

  • WAL vs. Maturity: WAL is not the same as the final maturity date. Maturity is the date the debt is fully due, while WAL is the average time until principal repayment, weighted by payment amounts. For a standard amortizing loan, WAL will be less than maturity. For a bullet bond (one principal payment at maturity), WAL equals maturity.
  • WAL vs. Duration: While both measure sensitivity to interest rates, duration measures price sensitivity to rate changes, whereas WAL focuses solely on the timing of principal repayment.
  • Ignoring Prepayments: WAL calculations can become complex if they need to account for potential prepayments (common in mortgage-backed securities). The examples here assume scheduled payments.

Weighted Average Life Formula and Mathematical Explanation

The Weighted Average Life (WAL) formula is a straightforward calculation that averages the repayment periods of a debt instrument, giving more weight to larger principal payments. This provides a realistic expectation of when an investor will receive their principal back.

The Core Formula

The fundamental formula for Weighted Average Life is:

WAL = Σ (Pi × Ti) / PP

Where:

  • WAL is the Weighted Average Life.
  • Σ denotes the summation of values.
  • Pi is the principal portion of the payment made at time i.
  • Ti is the time (in years) when the payment `i` is scheduled to be made.
  • PP is the total initial principal amount of the debt.

Step-by-Step Derivation

  1. Identify all scheduled principal payments: List every instance where a portion of the principal is expected to be repaid.
  2. Determine the timing of each payment: Note the exact point in time (usually in years from issuance) when each principal payment is due.
  3. Calculate the weighted payment for each period: For each payment, multiply the principal amount of that payment (Pi) by the time it is due (Ti). This gives you the 'weighted' component for that specific payment.
  4. Sum the weighted payments: Add up all the weighted payments calculated in the previous step. This gives you the numerator of the formula.
  5. Divide by the Total Principal: Divide the sum of the weighted payments by the original total principal amount of the debt instrument (PP).

The result is the Weighted Average Life, expressed in the same time units used for Ti (typically years).

Variables Table

Variable Meaning Unit Typical Range
WAL Weighted Average Life Years 0 to Maturity Date
Pi Principal portion of payment `i` Currency Units (e.g., USD) 0 to Total Principal
Ti Time of payment `i` Years 0 to Maturity Date
PP Total Initial Principal Amount Currency Units (e.g., USD) Positive Value

Practical Examples (Real-World Use Cases)

Understanding WAL is best done through examples. Let's consider two scenarios:

Example 1: Standard Amortizing Bond

Consider a bond with a principal amount of $1,000,000 that matures in 5 years. It has a sinking fund requiring equal principal repayments at the end of years 1, 2, 3, and 4, with the remaining principal paid at maturity (end of year 5). Each of the first four principal payments is $100,000.

  • Principal Amount (PP): $1,000,000
  • Total Scheduled Payments: 5

Payment Schedule:

  • Year 1 (T1=1): $100,000 principal (P1)
  • Year 2 (T2=2): $100,000 principal (P2)
  • Year 3 (T3=3): $100,000 principal (P3)
  • Year 4 (T4=4): $100,000 principal (P4)
  • Year 5 (T5=5): $600,000 principal (P5) – Remaining balance

Calculation:

  • Weighted Sum = (100,000 * 1) + (100,000 * 2) + (100,000 * 3) + (100,000 * 4) + (600,000 * 5)
  • Weighted Sum = 100,000 + 200,000 + 300,000 + 400,000 + 3,000,000 = $4,000,000
  • WAL = $4,000,000 / $1,000,000 = 4.0 years

Interpretation: The Weighted Average Life is 4.0 years. This means, on average, investors can expect to receive their principal back in 4 years, even though the final maturity is 5 years. The larger final payment significantly influences the average.

Example 2: Bullet Bond

Consider a simple corporate bond with a principal amount of $5,000,000 that pays only interest semi-annually and repays the entire principal at maturity in 10 years.

  • Principal Amount (PP): $5,000,000
  • Total Scheduled Payments: 1 (at maturity)

Payment Schedule:

  • Year 10 (T1=10): $5,000,000 principal (P1)

Calculation:

  • Weighted Sum = (5,000,000 * 10) = $50,000,000
  • WAL = $50,000,000 / $5,000,000 = 10.0 years

Interpretation: The Weighted Average Life is 10.0 years, which is equal to its maturity date. This is typical for bullet bonds where no principal is repaid until the final payment date.

How to Use This Weighted Average Life Calculator

Our Weighted Average Life calculator simplifies the process of determining the average principal repayment period for your debt instruments. Follow these simple steps:

Step-by-Step Guide:

  1. Enter Principal Amount: Input the total initial principal of the debt instrument into the 'Principal Amount' field. This is the total amount that needs to be repaid.
  2. Specify Number of Payments: Enter the total number of distinct periods in which principal payments are scheduled. For a bullet bond, this might be '1'. For an amortizing bond, it's the number of amortization payments plus the final balloon payment.
  3. Detail Each Payment: For each scheduled payment period (up to 5 are provided in the calculator, expand if needed for more complex instruments):
    • Enter the specific Payment Amount (principal portion only) for that period.
    • Enter the Time of Payment in years from the issuance date. For example, a payment at the end of the first year is '1'.
    Note: Ensure that the sum of all individual payment amounts equals the total 'Principal Amount' you entered initially. The calculator performs this check implicitly.
  4. View Results: Once inputs are entered, the results will update automatically in real-time.
  5. Understand the Output:
    • Primary Result (Weighted Average Life): This is the main output, shown in bold and highlighted. It represents the average time (in years) until the principal is repaid, weighted by payment size.
    • Total Principal: Confirms the initial principal amount entered.
    • Weighted Sum of Payments: The sum of (Payment Amount * Time of Payment) for all periods.
    • Total Payments Made: The sum of all individual principal payments entered. This should match the Total Principal.
  6. Use the Buttons:
    • Copy Results: Click this button to copy the main WAL result, intermediate values, and key assumptions to your clipboard for use elsewhere.
    • Reset: Click this button to clear all fields and revert to the default example values.

Decision-Making Guidance:

The WAL provides critical insights:

  • Comparing Investments: A lower WAL generally suggests faster principal recovery, which can reduce reinvestment risk and interest rate risk for the investor.
  • Risk Assessment: A WAL significantly shorter than the final maturity might indicate aggressive amortization or expected prepayments. A WAL equal to maturity points to a bullet repayment structure.
  • Cash Flow Planning: Understanding the WAL helps investors and issuers better forecast cash inflows and outflows.

Key Factors That Affect Weighted Average Life Results

Several factors influence the Weighted Average Life of a debt instrument. Understanding these helps in interpreting the results and assessing the underlying risks:

  1. Scheduled Amortization: The pre-defined schedule of principal repayments significantly impacts WAL. Loans with regular, increasing amortization payments will have a lower WAL compared to their maturity.
  2. Balloon Payments: A large final payment (balloon payment) at or near maturity will pull the WAL closer to the maturity date. If the balloon payment is substantial, WAL will be heavily weighted towards the later repayment times.
  3. Sinking Fund Provisions: Many bonds include sinking fund requirements, mandating periodic retirement of a portion of the debt before maturity. This feature actively reduces the WAL and provides investors with earlier principal recovery.
  4. Prepayment Speed Assumptions: For securities like mortgage-backed securities (MBS), homeowners may prepay their mortgages. Higher assumed prepayment speeds lead to a lower WAL because principal is returned to investors sooner than scheduled. Our calculator assumes scheduled payments, but real-world WAL analysis often incorporates prepayment models.
  5. Call Provisions: If an issuer has the right to "call" (redeem) the debt early, especially if interest rates fall, this can lead to earlier principal repayment than originally scheduled, thus shortening the WAL. Analysts often calculate WAL under various call scenarios.
  6. Interest Rate Environment: While WAL itself doesn't directly incorporate interest rates in its calculation, the *behavior* that affects repayment timing (like prepayments or calls triggered by refinancing) is heavily influenced by interest rates. Falling rates encourage prepayments and calls, reducing WAL. Rising rates tend to slow them down, increasing WAL.
  7. Original Issue Discount (OID) / Zero-Coupon Bonds: For bonds issued at a discount (OID) or zero-coupon bonds, the principal repayment happens entirely at maturity. Therefore, their WAL will always equal their maturity date, as there are no intermediate principal payments to weight.

Frequently Asked Questions (FAQ)

Q1: What's the difference between Weighted Average Life (WAL) and maturity?
Maturity is the final date when the entire principal of a debt instrument is due. WAL is the average time until principal is repaid, weighted by the amount of each repayment. For standard amortizing loans or bonds with sinking funds, WAL is typically less than maturity. For bullet bonds, WAL equals maturity.
Q2: Can WAL be longer than the maturity date?
No, by definition, WAL cannot be longer than the final maturity date because it's an average of repayment times, all of which occur at or before maturity.
Q3: Does WAL account for interest payments?
No, the WAL calculation focuses strictly on the timing and amount of principal repayments. Interest payments are separate cash flows and do not factor into the WAL calculation itself.
Q4: How is WAL calculated for mortgage-backed securities (MBS)?
Calculating WAL for MBS is more complex because it requires assumptions about prepayment speeds. Analysts model different prepayment scenarios (e.g., PSA standard) to estimate an expected WAL, as actual principal payments will vary based on homeowner behavior influenced by interest rates.
Q5: What does a WAL of 'X' years mean for an investor?
A WAL of 'X' years means that, on average, investors can expect to have received 'X' years' worth of their principal back. A shorter WAL implies faster recovery of invested capital, potentially reducing reinvestment risk.
Q6: Should I prefer an investment with a shorter WAL?
Not necessarily. A shorter WAL often means higher interest rate risk and reinvestment risk, as you receive principal back sooner and may need to reinvest it at potentially lower rates. Conversely, a longer WAL (closer to maturity) implies more certainty about the payment schedule but potentially higher exposure to interest rate fluctuations over a longer period. The preference depends on your investment horizon and risk tolerance.
Q7: How does the calculator handle multiple payments of the same amount?
The calculator requires you to input each payment and its specific time. If you have, for instance, five payments of $10,000 each occurring at years 1, 2, 3, 4, and 5, you would input each of those individually. The formula naturally weights them by their respective times.
Q8: What if the sum of my individual payments doesn't equal the total principal?
It's crucial that the sum of all principal payment amounts entered equals the initial total principal. If they don't match, the WAL calculation will be inaccurate. Ensure all principal is accounted for, whether through regular amortization or a final balloon payment.

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document.getElementById('totalPrincipalResult').textContent = '–'; document.getElementById('weightedSumResult').textContent = '–'; document.getElementById('totalPaymentsResult').textContent = '–'; updateChart([], []); // Clear chart return; } var wal = 0; if (totalPrincipal > 0) { wal = weightedSum / totalPrincipal; } document.getElementById('weightedAverageLifeResult').textContent = wal.toFixed(2) + ' years'; document.getElementById('totalPrincipalResult').textContent = principalAmount.toFixed(2); document.getElementById('weightedSumResult').textContent = weightedSum.toFixed(2); document.getElementById('totalPaymentsResult').textContent = sumOfPayments.toFixed(2); updateChart(chartDataTimes, chartDataPayments); } function resetForm() { document.getElementById('principalAmount').value = '1000000'; document.getElementById('paymentsInput').value = '5'; // Reset to 5 to show all default fields document.getElementById('payment1Amount').value = '150000'; document.getElementById('period1Time').value = '1'; document.getElementById('payment2Amount').value = '150000'; document.getElementById('period2Time').value = '2'; document.getElementById('payment3Amount').value = '150000'; document.getElementById('period3Time').value = '3'; document.getElementById('payment4Amount').value = '150000'; document.getElementById('period4Time').value = '4'; document.getElementById('payment5Amount').value = '400000'; // Make sure this sums up correctly with others document.getElementById('period5Time').value = '5'; // Clear errors var errorElements = document.querySelectorAll('.error-message'); for (var i = 0; i < errorElements.length; i++) { errorElements[i].textContent = ''; } calculateWAL(); // Recalculate with default values } function copyResults() { var walResult = document.getElementById('weightedAverageLifeResult').textContent; var totalPrincipal = document.getElementById('totalPrincipalResult').textContent; var weightedSum = document.getElementById('weightedSumResult').textContent; var totalPayments = document.getElementById('totalPaymentsResult').textContent; 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setTimeout(function() { copyButton.textContent = originalText; }, 2000); }, function(err) { console.error('Async: Could not copy text: ', err); alert('Failed to copy results. Please copy manually.'); }); } // Charting Logic (Pure SVG) var chartContainer = document.createElement('div'); chartContainer.id = 'walChartContainer'; chartContainer.style.marginTop = '30px'; document.getElementById('calculator-section').insertBefore(chartContainer, document.querySelectorAll('.article-section')[0]); function updateChart(times, payments) { var chartWrapper = document.getElementById('walChartContainer'); chartWrapper.innerHTML = ''; // Clear previous chart if (times.length === 0 || payments.length === 0) { return; // Don't draw if no data } var svgNS = "http://www.w3.org/2000/svg"; var svg = document.createElementNS(svgNS, "svg"); svg.setAttribute('viewBox', '0 0 400 250'); svg.style.width = '100%'; svg.style.height = 'auto'; svg.style.border = '1px solid var(–border-color)'; svg.style.borderRadius = '4px'; var caption = document.createElement('caption'); caption.textContent = 'Payment Amounts vs. Time'; chartWrapper.appendChild(caption); chartWrapper.appendChild(svg); 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svg.appendChild(xAxisGroup); var xAxisLine = document.createElementNS(svgNS, "line"); xAxisLine.setAttribute('x1', margin.left); xAxisLine.setAttribute('y1', chartHeight – margin.bottom); xAxisLine.setAttribute('x2', chartWidth – margin.right); xAxisLine.setAttribute('y2', chartHeight – margin.bottom); xAxisLine.setAttribute('stroke', '#666'); xAxisLine.setAttribute('stroke-width', '1'); xAxisGroup.appendChild(xAxisLine); // X-axis labels (simplified) var numXTicks = Math.min(times.length, 5); // Show up to 5 ticks or number of data points var xTickInterval = maxTime / numXTicks; for (var i = 0; i <= numXTicks; i++) { var tickValue = i * xTickInterval; var xPos = margin.left + (tickValue * xScale); var tickLabel = document.createElementNS(svgNS, "text"); tickLabel.setAttribute('x', xPos); tickLabel.setAttribute('y', chartHeight – margin.bottom + 15); tickLabel.setAttribute('text-anchor', 'middle'); tickLabel.setAttribute('font-size', '10px'); tickLabel.textContent = tickValue.toFixed(0); xAxisGroup.appendChild(tickLabel); var tickMark = document.createElementNS(svgNS, "line"); tickMark.setAttribute('x1', xPos); tickMark.setAttribute('y1', chartHeight – margin.bottom); tickMark.setAttribute('x2', xPos); tickMark.setAttribute('y2', chartHeight – margin.bottom + 5); tickMark.setAttribute('stroke', '#666'); tickMark.setAttribute('stroke-width', '1'); xAxisGroup.appendChild(tickMark); } // Add Y-axis label var yAxisLabel = document.createElementNS(svgNS, "text"); yAxisLabel.setAttribute('x', -(chartHeight / 2)); yAxisLabel.setAttribute('y', margin.left / 2); yAxisLabel.setAttribute('transform', 'rotate(-90)'); yAxisLabel.setAttribute('text-anchor', 'middle'); yAxisLabel.setAttribute('font-size', '12px'); yAxisLabel.textContent = 'Principal Amount'; svg.appendChild(yAxisLabel); // Add X-axis label var xAxisLabel = document.createElementNS(svgNS, "text"); xAxisLabel.setAttribute('x', margin.left + innerWidth / 2); xAxisLabel.setAttribute('y', chartHeight – margin.bottom / 2 + 10); xAxisLabel.setAttribute('text-anchor', 'middle'); xAxisLabel.setAttribute('font-size', '12px'); xAxisLabel.textContent = 'Time (Years)'; svg.appendChild(xAxisLabel); // Add points and lines var dataSeriesGroup = document.createElementNS(svgNS, "g"); svg.appendChild(dataSeriesGroup); var pathData = []; for (var i = 0; i < times.length; i++) { if (i < paymentsInput) { // Only plot points up to the specified number of payments var x = margin.left + times[i] * xScale; var y = chartHeight – margin.bottom – payments[i] * yScale; pathData.push(x + ',' + y); // Add circles for points var circle = document.createElementNS(svgNS, "circle"); circle.setAttribute('cx', x); circle.setAttribute('cy', y); circle.setAttribute('r', 4); circle.setAttribute('fill', 'var(–primary-color)'); dataSeriesGroup.appendChild(circle); // Add text labels for payment amounts above points var text = document.createElementNS(svgNS, "text"); text.setAttribute('x', x); text.setAttribute('y', y – 10); // Position above the point text.setAttribute('text-anchor', 'middle'); text.setAttribute('font-size', '9px'); text.setAttribute('fill', '#333'); text.textContent = payments[i].toFixed(0); dataSeriesGroup.appendChild(text); } } // Add line connecting points var polyline = document.createElementNS(svgNS, "polyline"); polyline.setAttribute('points', pathData.join(' ')); polyline.setAttribute('fill', 'none'); polyline.setAttribute('stroke', 'var(–primary-color)'); polyline.setAttribute('stroke-width', '2'); dataSeriesGroup.appendChild(polyline); // Add legend var legendGroup = document.createElementNS(svgNS, "g"); svg.appendChild(legendGroup); var legendRect = document.createElementNS(svgNS, "rect"); legendRect.setAttribute('x', chartWidth – margin.right – 110); legendRect.setAttribute('y', margin.top); legendRect.setAttribute('width', 15); legendRect.setAttribute('height', 15); legendRect.setAttribute('fill', 'var(–primary-color)'); legendGroup.appendChild(legendRect); var legendText = document.createElementNS(svgNS, "text"); legendText.setAttribute('x', chartWidth – margin.right – 110 + 20); legendText.setAttribute('y', margin.top + 12); legendText.setAttribute('font-size', '12px'); legendText.textContent = 'Payment Amount'; legendGroup.appendChild(legendText); } // Initial calculation and chart draw on page load document.addEventListener('DOMContentLoaded', function() { // Attach listeners to inputs to trigger recalculation var inputs = document.querySelectorAll('.loan-calc-container input'); for (var i = 0; i < inputs.length; i++) { inputs[i].addEventListener('input', calculateWAL); } // Also listen for change on the select element var selectInputs = document.querySelectorAll('.loan-calc-container select'); for (var i = 0; i < selectInputs.length; i++) { selectInputs[i].addEventListener('change', calculateWAL); } // Trigger initial calculation calculateWAL(); // Setup FAQ toggle var questions = document.querySelectorAll('.faq-item .question'); for (var i = 0; i < questions.length; i++) { questions[i].addEventListener('click', function() { var answer = this.nextElementSibling; if (answer.style.display === 'block') { answer.style.display = 'none'; } else { answer.style.display = 'block'; } }); } });

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