Select the variable you want to solve for, enter the other four values, and click "Compute Result".
Understanding the BA II Plus Time Value of Money (TVM) Logic
The Texas Instruments BA II Plus is a staple for finance professionals and students (CFA, CFP). Its core strength lies in solving Time Value of Money equations where five variables are interconnected. In the world of the BA II Plus, cash inflows are typically represented as positive numbers and cash outflows (like a deposit or a loan payment) are represented as negative numbers.
The Five Key Variables:
N: The total number of compounding periods (e.g., years x months per year).
I/Y: The annual interest rate or periodic yield, expressed as a percentage (not a decimal).
PV: Present Value – the current worth of a future sum of money or stream of cash flows.
PMT: Payment – the amount of the periodic payment made each period.
FV: Future Value – the value of an asset or cash at a specified date in the future.
Common Calculation Examples:
Example 1: Solving for Future Value (FV)
If you invest 1,000 (PV = -1,000) for 10 years (N = 10) at an 8% annual return (I/Y = 8), and make no additional payments (PMT = 0), what will it be worth? Result: FV = 2,158.92
Example 2: Solving for Payment (PMT)
You want to save 50,000 (FV = 50,000) over 5 years (N = 5) with a 6% interest rate (I/Y = 6). You starting with 0 (PV = 0). How much must you save annually? Result: PMT = -8,869.82
Tips for Using This Emulator
This online tool mimics the algebraic solver of the physical calculator. Remember the Cash Flow Convention: If you receive money, it's a positive. If you pay or invest it, it's a negative. If your calculation returns a "NaN" or error, ensure you aren't leaving essential fields blank and that interest rates are above zero for N calculations.
function calculateBAII() {
var n = parseFloat(document.getElementById("input_N").value);
var i_y = parseFloat(document.getElementById("input_IY").value);
var pv = parseFloat(document.getElementById("input_PV").value);
var pmt = parseFloat(document.getElementById("input_PMT").value);
var fv = parseFloat(document.getElementById("input_FV").value);
var solveFor = document.querySelector('input[name="solveVar"]:checked').value;
var resultDiv = document.getElementById("calculator_result");
var result = 0;
var r = i_y / 100;
try {
if (solveFor === "FV") {
if (r === 0) {
result = -(pv + (pmt * n));
} else {
result = -(pv * Math.pow(1 + r, n) + pmt * (Math.pow(1 + r, n) – 1) / r);
}
resultDiv.innerHTML = "Calculated Future Value (FV): " + result.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
}
else if (solveFor === "PV") {
if (r === 0) {
result = -(fv + (pmt * n));
} else {
result = -(fv / Math.pow(1 + r, n) + pmt * (Math.pow(1 + r, n) – 1) / (r * Math.pow(1 + r, n)));
}
resultDiv.innerHTML = "Calculated Present Value (PV): " + result.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
}
else if (solveFor === "PMT") {
if (r === 0) {
result = -(pv + fv) / n;
} else {
result = -(pv * Math.pow(1 + r, n) + fv) / ((Math.pow(1 + r, n) – 1) / r);
}
resultDiv.innerHTML = "Calculated Payment (PMT): " + result.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
}
else if (solveFor === "N") {
if (r === 0) {
result = -(pv + fv) / pmt;
} else {
var numerator = (pmt – fv * r);
var denominator = (pmt + pv * r);
if (numerator / denominator <= 0) {
resultDiv.innerHTML = "Error: Invalid inputs for N calculation (Check signs)";
resultDiv.style.display = "block";
return;
}
result = Math.log(numerator / denominator) / Math.log(1 + r);
}
resultDiv.innerHTML = "Calculated Number of Periods (N): " + result.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
}
else if (solveFor === "IY") {
// Iterative solution for Interest Rate (Rate of Return)
var rate = 0.1; // Initial guess
for (var iter = 0; iter < 100; iter++) {
var f = pv * Math.pow(1 + rate, n) + pmt * (Math.pow(1 + rate, n) – 1) / rate + fv;
var f_prime = n * pv * Math.pow(1 + rate, n – 1) + pmt * (n * rate * Math.pow(1 + rate, n – 1) – Math.pow(1 + rate, n) + 1) / (rate * rate);
var newRate = rate – f / f_prime;
if (Math.abs(newRate – rate) < 0.0000001) {
rate = newRate;
break;
}
rate = newRate;
}
result = rate * 100;
resultDiv.innerHTML = "Calculated Interest Rate (I/Y): " + result.toLocaleString(undefined, {minimumFractionDigits: 3, maximumFractionDigits: 3}) + "%";
}
if (isNaN(result)) {
resultDiv.innerHTML = "Error: Please check all required numeric inputs.";
}
resultDiv.style.display = "block";
} catch (e) {
resultDiv.innerHTML = "Calculation Error. Check signs (+/-).";
resultDiv.style.display = "block";
}
}