TVM Calculator
:root {
–primary-blue: #004a99;
–success-green: #28a745;
–light-background: #f8f9fa;
–border-color: #dee2e6;
–text-color: #343a40;
–label-color: #495057;
}
body {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
line-height: 1.6;
color: var(–text-color);
background-color: var(–light-background);
margin: 0;
padding: 20px;
}
.loan-calc-container {
max-width: 800px;
margin: 30px auto;
padding: 30px;
background-color: #ffffff;
border-radius: 8px;
box-shadow: 0 4px 15px rgba(0, 0, 0, 0.08);
border: 1px solid var(–border-color);
}
h1, h2 {
color: var(–primary-blue);
text-align: center;
margin-bottom: 20px;
}
.input-group {
margin-bottom: 20px;
padding: 15px;
border: 1px solid var(–border-color);
border-radius: 5px;
background-color: #fff;
transition: box-shadow 0.3s ease;
}
.input-group:hover {
box-shadow: 0 2px 10px rgba(0, 74, 153, 0.1);
}
.input-group label {
display: block;
margin-bottom: 8px;
font-weight: 600;
color: var(–label-color);
font-size: 0.95em;
}
.input-group input[type="number"],
.input-group input[type="text"],
.input-group select {
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padding: 12px 10px;
border: 1px solid var(–border-color);
border-radius: 4px;
font-size: 1em;
color: var(–text-color);
box-sizing: border-box; /* Include padding and border in the element's total width and height */
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.input-group input[type="number"]:focus,
.input-group input[type="text"]:focus,
.input-group select:focus {
outline: none;
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text-align: center;
margin-top: 25px;
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button {
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color: white;
padding: 12px 25px;
border: none;
border-radius: 5px;
font-size: 1.1em;
cursor: pointer;
transition: background-color 0.3s ease, transform 0.2s ease;
margin: 0 10px;
}
button:hover {
background-color: #003f80;
transform: translateY(-2px);
}
button:active {
transform: translateY(0);
}
#result {
margin-top: 30px;
padding: 25px;
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color: white;
text-align: center;
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font-size: 1.5em;
font-weight: bold;
box-shadow: 0 4px 15px rgba(40, 167, 69, 0.3);
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.explanation {
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.explanation h2 {
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margin-bottom: 15px;
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.explanation p, .explanation ul, .explanation li {
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border-radius: 3px;
font-family: Consolas, Monaco, 'Andale Mono', 'Ubuntu Mono', monospace;
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/* Responsive adjustments */
@media (max-width: 768px) {
.loan-calc-container {
padding: 20px;
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button {
width: 90%;
margin-bottom: 10px;
margin-left: 5%;
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#result {
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}
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padding: 15px;
}
h1 {
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#result {
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}
.input-group input[type="number"],
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width: calc(100% – 10px);
padding: 10px 5px;
}
}
TI BA II Plus Professional TVM Calculator
Number of Periods (N)
Interest Rate per Period (I/Y)
Present Value (PV)
Payment per Period (PMT)
Future Value (FV)
Payment Timing
End of Period (Ordinary Annuity)
Beginning of Period (Annuity Due)
Compute N
Compute I/Y
Compute PV
Compute PMT
Compute FV
Understanding the TI BA II Plus Professional TVM Calculator
The Texas Instruments BA II Plus Professional is a popular financial calculator widely used for business and finance calculations. Its core functionality revolves around Time Value of Money (TVM) calculations, which help in understanding the relationship between money, time, and interest rates. The calculator solves for one of the five key TVM variables (N, I/Y, PV, PMT, FV) when the other four are known, assuming a constant interest rate and regular payments.
The Five TVM Variables Explained:
N (Number of Periods): This represents the total number of payment or compounding periods. For example, if you're calculating a 30-year mortgage with monthly payments, N would be 30 years * 12 months/year = 360 periods.I/Y (Interest Rate per Period): This is the interest rate applied during each period. It's crucial to express this as a rate per period . If you have an annual interest rate of 6% and monthly payments, the I/Y would be 6% / 12 = 0.5%. The calculator typically expects this as a percentage value (e.g., 0.5, not 0.005).PV (Present Value): This is the current worth of a future sum of money or a stream of cash flows given a specified rate of return. It's the value of an investment today. If you're taking out a loan, the loan amount is the PV (often entered as a negative value, signifying an outflow).PMT (Payment per Period): This is the constant amount of cash flow paid or received during each period. This could be a loan payment, an annuity payment, or a deposit. Like PV, it's often entered as negative if it represents an outflow (e.g., paying a loan).FV (Future Value): This is the value of an asset or cash at a specified date in the future, based on an assumed rate of growth. It's the final lump sum amount an investment will grow to, or the amount remaining on a loan after all payments are made.
Payment Timing: End vs. Beginning
The calculator differentiates between two types of annuities:
End of Period (Ordinary Annuity): Payments are made at the end of each period. This is the most common for loans and standard investments.Beginning of Period (Annuity Due): Payments are made at the beginning of each period. This often applies to things like lease payments or certain types of savings plans where money is deposited upfront.
The Math Behind TVM Calculations
The fundamental TVM equation that the calculator solves is:
$$ PV \times (1 + \frac{I}{100})^N + PMT \times \frac{1 – (1 + \frac{I}{100})^N}{ \frac{I}{100}} \times \text{TimingFactor} + FV = 0 $$
Where:
I is the annual interest rate (as a percentage). The calculator internally converts this to the rate per period.TimingFactor is 1 for End of Period (Ordinary Annuity) and (1 + I/100) for Beginning of Period (Annuity Due).
The calculator rearranges this formula to solve for the unknown variable. For example, to solve for PV:
$$ PV = – [ PMT \times \frac{1 – (1 + \frac{I}{100})^{-N}}{ \frac{I}{100}} \times \text{TimingFactor} + FV \times (1 + \frac{I}{100})^{-N} ] $$
This online calculator simulates this process by taking your inputs and calculating the missing variable using the same logic.
Common Use Cases:
Mortgage calculations (finding loan payments, total interest paid)
Loan amortization schedules
Retirement planning (calculating future savings, required contributions)
Lease evaluations
Bond pricing
Investment analysis
function calculateTVM(computeVar) {
var n = parseFloat(document.getElementById('n').value);
var i_percent = parseFloat(document.getElementById('i').value); // Input is percentage, e.g., 5 for 5%
var pv = parseFloat(document.getElementById('pv').value);
var pmt = parseFloat(document.getElementById('pmt').value);
var fv = parseFloat(document.getElementById('fv').value);
var payment_timing = document.getElementById('payment_timing').value;
var resultDisplay = document.getElementById('result');
resultDisplay.textContent = "; // Clear previous result
// Basic validation
var inputsProvided = 0;
var missingVar = ";
if (isNaN(n)) { n = null; } else { inputsProvided++; }
if (isNaN(i_percent)) { i_percent = null; } else { inputsProvided++; }
if (isNaN(pv)) { pv = null; } else { inputsProvided++; }
if (isNaN(pmt)) { pmt = null; } else { inputsProvided++; }
if (isNaN(fv)) { fv = null; } else { inputsProvided++; }
if (inputsProvided < 4) {
resultDisplay.textContent = "Please provide values for at least 4 variables.";
return;
}
var i_decimal = (i_percent === null) ? null : i_percent / 100.0; // Rate per period as decimal
var timing_factor = 1.0;
if (payment_timing === 'begin' && i_decimal !== null) {
timing_factor = 1.0 + i_decimal;
}
var calculatedValue = null;
try {
if (computeVar === 'n') {
if (n === null && i_decimal !== null && pv !== null && pmt !== null && fv !== null) {
if (pmt === 0 && pv === 0 && fv === 0) {
resultDisplay.textContent = "Cannot solve for N when PV, PMT, and FV are all zero.";
return;
}
// Handle edge case where (pv + fv / timing_factor) / pmt may not be calculable if denominator is zero or leads to invalid log
var term1 = (pmt !== 0) ? pmt * timing_factor : 0;
var term2 = (i_decimal !== 0) ? (i_decimal + 1) : 1; // Handle i=0 case
var numeratorForLog = (pv === 0 && fv === 0 && pmt === 0) ? 1 : ((fv === 0) ? 1 : (fv + term1) / term1); // Simplified for edge cases
if (i_decimal === 0) { // Special case for 0 interest rate
if (pmt === 0) {
if (pv === fv) {
calculatedValue = 0; // Indeterminate, or infinite periods needed if PV != FV
} else {
resultDisplay.textContent = "Cannot solve for N with 0% interest and PV != FV.";
return;
}
} else {
calculatedValue = -(pv + fv) / pmt;
}
} else {
var logBase = 1 + i_decimal;
var numerator = (fv === null) ? term1 : (term1 + fv);
if (numerator === 0 && term1 === 0) { // Only if pmt is 0
calculatedValue = null; // Cannot solve if pmt is 0 and fv is 0
} else {
var ratio = (pv === null) ? numerator / term1 : (numerator – pv) / term1;
if (ratio <= 0) {
resultDisplay.textContent = "Cannot solve for N. Logarithm of non-positive number.";
return;
}
calculatedValue = Math.log(ratio) / Math.log(logBase);
}
}
if (calculatedValue !== null) {
document.getElementById('n').value = calculatedValue.toFixed(4);
resultDisplay.textContent = "N = " + calculatedValue.toFixed(4);
} else {
resultDisplay.textContent = "Could not calculate N.";
}
} else {
resultDisplay.textContent = "Provide N, I/Y, PV, PMT, and FV to compute N.";
}
} else if (computeVar === 'i') {
if (i_decimal === null && n !== null && pv !== null && pmt !== null && fv !== null) {
// Numerical method required here as I/Y cannot be solved directly algebraically.
// For simplicity in this JS example, we'll inform the user.
resultDisplay.textContent = "Solving for I/Y requires iterative methods not implemented here. Use the physical calculator.";
return;
} else {
resultDisplay.textContent = "Provide N, I/Y, PV, PMT, and FV to compute I/Y.";
}
} else if (computeVar === 'pv') {
if (pv === null && n !== null && i_decimal !== null && pmt !== null && fv !== null) {
if (i_decimal === 0) {
calculatedValue = -(pmt * n + fv);
} else {
var factor = Math.pow(1 + i_decimal, n);
calculatedValue = -(pmt * (1 – Math.pow(1 + i_decimal, -n)) / i_decimal * timing_factor + fv / factor);
}
document.getElementById('pv').value = calculatedValue.toFixed(2);
resultDisplay.textContent = "PV = " + calculatedValue.toFixed(2);
} else {
resultDisplay.textContent = "Provide N, I/Y, PV, PMT, and FV to compute PV.";
}
} else if (computeVar === 'pmt') {
if (pmt === null && n !== null && i_decimal !== null && pv !== null && fv !== null) {
if (i_decimal === 0) {
calculatedValue = (n === 0) ? 0 : -(pv + fv) / n;
} else {
var factor = Math.pow(1 + i_decimal, n);
calculatedValue = – (pv * Math.pow(1 + i_decimal, n) + fv) * i_decimal / (timing_factor * (factor – 1));
}
document.getElementById('pmt').value = calculatedValue.toFixed(2);
resultDisplay.textContent = "PMT = " + calculatedValue.toFixed(2);
} else {
resultDisplay.textContent = "Provide N, I/Y, PV, PMT, and FV to compute PMT.";
}
} else if (computeVar === 'fv') {
if (fv === null && n !== null && i_decimal !== null && pv !== null && pmt !== null) {
if (i_decimal === 0) {
calculatedValue = -(pv + pmt * n);
} else {
var factor = Math.pow(1 + i_decimal, n);
calculatedValue = -(pv * factor + pmt * (factor – 1) / i_decimal * timing_factor);
}
document.getElementById('fv').value = calculatedValue.toFixed(2);
resultDisplay.textContent = "FV = " + calculatedValue.toFixed(2);
} else {
resultDisplay.textContent = "Provide N, I/Y, PV, PMT, and FV to compute FV.";
}
}
} catch (e) {
resultDisplay.textContent = "Calculation Error: " + e.message;
}
}