Use this calculator to solve for any of the five Time Value of Money (TVM) variables: Number of Periods (N), Annual Rate (I/Y), Present Value (PV), Payment (PMT), or Future Value (FV). Leave the variable you wish to solve for blank.
/* Basic styling for the calculator */
.calculator-container {
font-family: Arial, sans-serif;
max-width: 600px;
margin: 20px auto;
padding: 20px;
border: 1px solid #ccc;
border-radius: 8px;
background-color: #f9f9f9;
}
.calculator-container h2 {
text-align: center;
color: #333;
margin-bottom: 20px;
}
.calc-input-group {
margin-bottom: 15px;
}
.calc-input-group label {
display: block;
margin-bottom: 5px;
font-weight: bold;
color: #555;
}
.calc-input-group input[type="number"],
.calc-input-group select {
width: calc(100% – 22px);
padding: 10px;
border: 1px solid #ddd;
border-radius: 4px;
box-sizing: border-box;
}
.calc-input-group input[type="radio"] {
margin-right: 5px;
}
.calc-input-group input[type="radio"] + label {
display: inline-block;
font-weight: normal;
margin-right: 15px;
}
button {
background-color: #007bff;
color: white;
padding: 12px 20px;
border: none;
border-radius: 4px;
cursor: pointer;
font-size: 16px;
margin-right: 10px;
}
button:hover {
background-color: #0056b3;
}
button:last-of-type {
background-color: #6c757d;
}
button:last-of-type:hover {
background-color: #5a6268;
}
.calc-result {
margin-top: 20px;
padding: 15px;
border: 1px solid #e0e0e0;
border-radius: 4px;
background-color: #e9ecef;
color: #333;
font-size: 1.1em;
font-weight: bold;
}
.calc-result p {
margin: 0;
}
function calculateTVM() {
var n_str = document.getElementById("numPeriods").value;
var i_str = document.getElementById("annualRate").value;
var pv_str = document.getElementById("presentValue").value;
var pmt_str = document.getElementById("payment").value;
var fv_str = document.getElementById("futureValue").value;
var frequency = parseFloat(document.getElementById("frequency").value);
var paymentTimingBegin = document.getElementById("paymentTimingBegin").checked;
var inputs = [n_str, i_str, pv_str, pmt_str, fv_str];
var blankCount = inputs.filter(function(val) { return val === ""; }).length;
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = "";
if (blankCount !== 1) {
resultDiv.innerHTML = "Please leave exactly one field blank to solve for.";
return;
}
var n = n_str === "" ? NaN : parseFloat(n_str);
var i_annual = i_str === "" ? NaN : parseFloat(i_str);
var pv = pv_str === "" ? NaN : parseFloat(pv_str);
var pmt = pmt_str === "" ? NaN : parseFloat(pmt_str);
var fv = fv_str === "" ? NaN : parseFloat(fv_str);
if (isNaN(frequency) || frequency <= 0) {
resultDiv.innerHTML = "Invalid compounding/payment frequency.";
return;
}
// Convert annual rate to periodic rate
var i_periodic;
if (!isNaN(i_annual)) {
i_periodic = i_annual / (100 * frequency);
}
var BGN = paymentTimingBegin ? 1 : 0;
// Function to calculate FV given N, i, PV, PMT
function calculateFV(n_val, i_per, pv_val, pmt_val, BGN_val) {
if (i_per === 0) {
return – (pv_val + pmt_val * n_val);
}
var term = Math.pow(1 + i_per, n_val);
var fv_calc = – (pv_val * term + pmt_val * ((term – 1) / i_per) * (1 + i_per * BGN_val));
return fv_calc;
}
// Function to calculate PV given N, i, PMT, FV
function calculatePV(n_val, i_per, pmt_val, fv_val, BGN_val) {
if (i_per === 0) {
return – (fv_val + pmt_val * n_val);
}
var term = Math.pow(1 + i_per, n_val);
var pv_calc = – (fv_val + pmt_val * ((term – 1) / i_per) * (1 + i_per * BGN_val)) / term;
return pv_calc;
}
// Function to calculate PMT given N, i, PV, FV
function calculatePMT(n_val, i_per, pv_val, fv_val, BGN_val) {
if (i_per === 0) {
if (n_val === 0) return NaN; // Cannot solve if no periods
return – (pv_val + fv_val) / n_val;
}
var term = Math.pow(1 + i_per, n_val);
var pmt_factor = ((term – 1) / i_per) * (1 + i_per * BGN_val);
if (pmt_factor === 0) return NaN; // Avoid division by zero if factor is zero
var pmt_calc = – (fv_val + pv_val * term) / pmt_factor;
return pmt_calc;
}
// Function to calculate N given i, PV, PMT, FV
function calculateN(i_per, pv_val, pmt_val, fv_val, BGN_val) {
if (i_per === 0) {
if (pmt_val === 0) return NaN; // Cannot solve if no payments and no interest
return – (pv_val + fv_val) / pmt_val;
}
var num = pmt_val * (1 + i_per * BGN_val) – fv_val * i_per;
var den = pmt_val * (1 + i_per * BGN_val) + pv_val * i_per;
if (num <= 0 || den <= 0 || (num / den) <= 0) { // Logarithm of non-positive number
return NaN;
}
var n_calc = Math.log(num / den) / Math.log(1 + i_per);
return n_calc;
}
// Function to calculate I/Y (iterative solver)
function calculateI(n_val, pv_val, pmt_val, fv_val, BGN_val, freq_val) {
// Newton-Raphson method
var guess = 0.05 / freq_val; // Initial guess for periodic rate (5% annual)
if (n_val === 0) return NaN; // Cannot solve for rate if no periods
// Check for i=0 case first
// If i=0, TVM equation simplifies to FV + PV + PMT*N = 0
var check_i_zero_val = pv_val + pmt_val * n_val + fv_val;
if (Math.abs(check_i_zero_val) < 1e-6) { // If i=0 is a solution
return 0;
}
var maxIterations = 1000;
var tolerance = 1e-7;
for (var iter = 0; iter < maxIterations; iter++) {
var term = Math.pow(1 + guess, n_val);
var f_i = pv_val * term + pmt_val * ((term – 1) / guess) * (1 + guess * BGN_val) + fv_val;
var df_di;
if (Math.abs(guess) < 1e-9) { // If guess is very close to zero
// Derivative of f(i) at i=0: PV*N + PMT*N*BGN
df_di = pv_val * n_val + pmt_val * n_val * BGN_val;
} else {
df_di = pv_val * n_val * term / (1 + guess) + pmt_val * (
(n_val * term * guess – (term – 1)) / (guess * guess) * (1 + guess * BGN_val) +
((term – 1) / guess) * BGN_val
);
}
if (Math.abs(df_di) < 1e-10) {
// If derivative is too small, the function is flat, or we are at a local extremum.
// This often means no real solution or multiple solutions.
return NaN;
}
var next_guess = guess – f_i / df_di;
if (Math.abs(next_guess – guess) < tolerance) {
return next_guess * freq_val * 100; // Convert periodic rate back to annual percentage
}
guess = next_guess;
}
return NaN; // Did not converge
}
var solvedValue;
var solvedFor = "";
if (isNaN(fv)) {
solvedValue = calculateFV(n, i_periodic, pv, pmt, BGN);
solvedFor = "Future Value (FV)";
} else if (isNaN(pv)) {
solvedValue = calculatePV(n, i_periodic, pmt, fv, BGN);
solvedFor = "Present Value (PV)";
} else if (isNaN(pmt)) {
solvedValue = calculatePMT(n, i_periodic, pv, fv, BGN);
solvedFor = "Payment per Period (PMT)";
} else if (isNaN(n)) {
solvedValue = calculateN(i_periodic, pv, pmt, fv, BGN);
solvedFor = "Number of Periods (N)";
} else if (isNaN(i_annual)) {
solvedValue = calculateI(n, pv, pmt, fv, BGN, frequency);
solvedFor = "Annual Rate (I/Y)";
}
if (isNaN(solvedValue)) {
resultDiv.innerHTML = "Could not calculate " + solvedFor + ". Please check your inputs. Ensure PMT is negative if it's an outflow, and PV/FV signs are consistent (e.g., PV positive, FV negative for a loan).";
} else {
var formattedValue;
if (solvedFor.includes("Value") || solvedFor.includes("Payment")) {
formattedValue = "$" + solvedValue.toFixed(2);
} else if (solvedFor.includes("Rate")) {
formattedValue = solvedValue.toFixed(4) + "%"; // More precision for rate
} else { // N
formattedValue = solvedValue.toFixed(2);
}
resultDiv.innerHTML = "" + solvedFor + ": " + formattedValue + "";
}
}
function clearInputs() {
document.getElementById("numPeriods").value = "";
document.getElementById("annualRate").value = "";
document.getElementById("presentValue").value = "";
document.getElementById("payment").value = "";
document.getElementById("futureValue").value = "";
document.getElementById("frequency").value = "12"; // Reset to monthly
document.getElementById("paymentTimingEnd").checked = true;
document.getElementById("result").innerHTML = "";
}
Understanding the Texas Instruments BA II Plus TVM Calculator
The Texas Instruments BA II Plus is a widely used financial calculator, especially popular among finance professionals, students, and those preparing for exams like the CFA. Its core functionality revolves around Time Value of Money (TVM) calculations, which allow you to determine the value of money over time, considering factors like growth rates and periodic payments.
This online calculator emulates the TVM functions of the BA II Plus, enabling you to solve for any one of the five key financial variables when the other four are known. This is incredibly useful for analyzing loans, investments, annuities, and more.
How to Use This Calculator
To use the calculator, simply enter values for four of the five main TVM variables (N, I/Y, PV, PMT, FV) and leave the field you wish to solve for blank. The calculator will then compute the missing value.
Number of Periods (N): This represents the total number of compounding or payment periods over the life of the investment or loan. For example, a 30-year loan with monthly payments would have N = 30 * 12 = 360 periods.
Annual Rate (%) (I/Y): This is the annual percentage rate (APR) or annual yield. The calculator will automatically adjust this to a periodic rate based on your selected "Compounding/Payment Frequency per Year."
Present Value ($) (PV): The current value of a future sum of money or stream of cash flows. This is often the initial amount of a loan or investment. Typically, money received (like a loan principal) is entered as a positive value, and money paid out (like an investment) as a negative value.
Payment per Period ($) (PMT): The amount of each regular payment made or received. For a loan, this would be your monthly payment. For an investment, it could be a regular contribution. Payments are usually entered with the opposite sign of the Present Value (e.g., if PV is positive, PMT is negative).
Future Value ($) (FV): The value of an asset or cash at a specified time in the future. For a loan, this is often 0 (meaning the loan is paid off). For an investment, it's the accumulated value at the end of the period.
Compounding/Payment Frequency per Year: This determines how many times per year the interest is compounded and/or payments are made. Common frequencies include Monthly (12), Quarterly (4), or Annually (1).
Payment Timing:
End of Period (Ordinary Annuity): Payments are made at the end of each period. This is the most common scenario for loans and bonds.
Beginning of Period (Annuity Due): Payments are made at the beginning of each period. This is common for leases or rent payments.
Important Sign Conventions
Just like the physical BA II Plus calculator, this tool uses sign conventions to distinguish between cash inflows and outflows. It's crucial to be consistent:
Outflows (money leaving your pocket): Typically entered as negative values (e.g., loan payments, initial investment).
Inflows (money coming into your pocket): Typically entered as positive values (e.g., loan principal received, future value of an investment).
For example, if you borrow $100,000 (PV = 100,000), your payments will be outflows (PMT = -X). If you invest $1,000 (PV = -1,000), and want to know its future value, FV will be positive.
Examples
Example 1: Calculating Loan Payment (PMT)
You want to take out a $200,000 loan for 30 years at an annual rate of 4.5%, compounded monthly. What will your monthly payment be?
N: 30 * 12 = 360
I/Y: 4.5
PV: 200000
PMT: (Leave blank)
FV: 0 (loan is paid off)
Frequency: Monthly (12)
Payment Timing: End of Period
Result: PMT should be approximately -$1,013.37 (an outflow).
Example 2: Calculating Future Value (FV) of an Investment
You invest $5,000 today and plan to contribute an additional $100 at the beginning of each month for the next 10 years. Your investment earns an annual return of 7%, compounded monthly. What will be the future value of your investment?
N: 10 * 12 = 120
I/Y: 7
PV: -5000 (initial investment is an outflow)
PMT: -100 (monthly contributions are outflows)
FV: (Leave blank)
Frequency: Monthly (12)
Payment Timing: Beginning of Period
Result: FV should be approximately $24,476.90 (an inflow).
Example 3: Calculating Annual Rate (I/Y)
You invested $10,000 five years ago. You made no additional payments, and today your investment is worth $13,000. What was your annual rate of return, compounded annually?