The BA II Plus is the industry standard for financial professionals, CFA candidates, and business students. Unlike a standard scientific calculator, it features a dedicated row for Time Value of Money (TVM) calculations. This allows users to solve for missing variables in complex financial scenarios like mortgages, car loans, and investment growth.
The 5 Key TVM Buttons
N: The total number of compounding periods (e.g., years × payments per year).
I/Y: The nominal annual interest rate (entered as a whole number, e.g., 5 for 5%).
PV: The Present Value. This is usually the loan amount (positive if receiving cash) or initial investment (negative if paying out).
PMT: The periodic payment amount.
FV: The Future Value or cash balance remaining after the last payment is made.
Real-World Example: Calculating a Car Loan
Suppose you want to buy a car for 30,000. You are offered a 5-year loan at an interest rate of 4.5%. What is your monthly payment?
N: 60 (5 years × 12 months)
I/Y: 4.5
PV: 30,000
FV: 0
P/Y: 12
Action: Compute (CPT) PMT. The result would be approximately -559.29 (negative because it is a cash outflow).
Cash Flow Sign Convention
A crucial rule of the BA II Plus logic is that money coming in is a positive number, and money going out is a negative number. If you enter both PV and FV as positive numbers when solving for interest rate, the calculator will return an error because it assumes you received money twice without ever paying it back.
function clearBA() {
document.getElementById('ba_n').value = ";
document.getElementById('ba_iy').value = ";
document.getElementById('ba_pv').value = ";
document.getElementById('ba_pmt').value = ";
document.getElementById('ba_fv').value = ";
document.getElementById('ba_result_container').style.display = 'none';
}
function calculateBA(target) {
var n = parseFloat(document.getElementById('ba_n').value) || 0;
var iy = parseFloat(document.getElementById('ba_iy').value) || 0;
var pv = parseFloat(document.getElementById('ba_pv').value) || 0;
var pmt = parseFloat(document.getElementById('ba_pmt').value) || 0;
var fv = parseFloat(document.getElementById('ba_fv').value) || 0;
var py = parseFloat(document.getElementById('ba_py').value) || 1;
var type = parseInt(document.getElementById('ba_timing').value);
var r = (iy / 100) / py;
var result = 0;
try {
if (target === 'PV') {
if (r === 0) {
result = -(fv + pmt * n);
} else {
var df = Math.pow(1 + r, n);
var annuityFactor = (1 – (1 / df)) / r;
if (type === 1) annuityFactor *= (1 + r);
result = -(fv / df + pmt * annuityFactor);
}
document.getElementById('ba_pv').value = result.toFixed(4);
}
else if (target === 'FV') {
if (r === 0) {
result = -(pv + pmt * n);
} else {
var df = Math.pow(1 + r, n);
var annuityFactor = (df – 1) / r;
if (type === 1) annuityFactor *= (1 + r);
result = -(pv * df + pmt * annuityFactor);
}
document.getElementById('ba_fv').value = result.toFixed(4);
}
else if (target === 'PMT') {
if (r === 0) {
result = -(pv + fv) / n;
} else {
var df = Math.pow(1 + r, n);
var annuityFactor = (1 – (1 / df)) / r;
if (type === 1) annuityFactor *= (1 + r);
result = -(pv + fv / df) / annuityFactor;
}
document.getElementById('ba_pmt').value = result.toFixed(4);
}
else if (target === 'N') {
if (r === 0) {
result = -(pv + fv) / pmt;
} else {
var adjPmt = (type === 1) ? pmt * (1 + r) : pmt;
var numerator = adjPmt – fv * r;
var denominator = adjPmt + pv * r;
result = Math.log(numerator / denominator) / Math.log(1 + r);
}
document.getElementById('ba_n').value = result.toFixed(4);
}
else if (target === 'IY') {
// Newton-Raphson method for Rate
var rate = 0.1 / py;
var iteration = 0;
var maxIterations = 100;
var precision = 0.0000001;
for (var i = 0; i < maxIterations; i++) {
var df = Math.pow(1 + rate, n);
var df_prev = Math.pow(1 + rate, n – 1);
var ann = (type === 1) ? (1 + rate) : 1;
// Function f(r)
var f = pv * df + pmt * ann * ((df – 1) / rate) + fv;
// Derivative f'(r)
var d_ann = (type === 1) ? 1 : 0;
var f_prime = n * pv * df_prev + pmt * (ann * (n * df_prev * rate – (df – 1)) / (rate * rate) + d_ann * (df – 1) / rate);
var newRate = rate – f / f_prime;
if (Math.abs(newRate – rate) < precision) {
rate = newRate;
break;
}
rate = newRate;
}
result = rate * py * 100;
document.getElementById('ba_iy').value = result.toFixed(4);
}
document.getElementById('ba_result_label').innerText = "Computed " + target;
document.getElementById('ba_result_val').innerText = result.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 4});
document.getElementById('ba_result_container').style.display = 'block';
} catch (e) {
alert("Error: Please check your inputs. Ensure signs (PV/FV/PMT) are correct for the cash flow direction.");
}
}