End of Period (Ordinary Annuity)
Beginning of Period (Annuity Due)
Enter values and click a calculation button.
Understanding the TI BA II Plus Professional Financial Calculator Functions
The TI BA II Plus Professional is a powerful financial calculator designed for business and finance professionals, students, and anyone who needs to perform complex financial calculations efficiently. It goes beyond basic arithmetic, offering dedicated functions for time value of money (TVM), cash flow analysis, amortization, and more. This calculator simulates the core TVM functionalities of such a device, allowing you to solve for one unknown variable when the others are known.
Key Variables Explained:
Present Value (PV): The current worth of a future sum of money or stream of cash flows, given a specified rate of return. It's what a future amount is worth today.
Future Value (FV): The value of an asset or cash at a specified date in the future, based on an assumed rate of growth. It's what an investment will be worth at a future date.
Payment per Period (PMT): The amount of a periodic payment, such as an annuity payment or loan payment. This is typically an outflow, hence often entered as a negative number.
Number of Periods (N): The total number of compounding or payment periods over the life of an investment or loan.
Interest Rate per Period (I/Y): The interest rate charged or earned per compounding period. This is usually entered as a percentage. The calculator (and this simulation) will convert it to a decimal for internal calculations.
Payment Frequency: Determines how many payments occur within a year. This is crucial because the interest rate and number of periods often need to be adjusted to match the payment frequency (e.g., if you have monthly payments, you'll need the monthly interest rate and the total number of months).
Payment Timing: Specifies whether payments occur at the beginning (Annuity Due) or end (Ordinary Annuity) of each period. This affects the total interest earned or paid.
The Math Behind the Calculations (Time Value of Money – TVM):
The core of these financial calculations is the Time Value of Money (TVM) formula. The fundamental equation that links these variables for an ordinary annuity (payments at the end of the period) is:
FV = PV * (1 + i)^n + PMT * [((1 + i)^n – 1) / i]
Where:
FV = Future Value
PV = Present Value
i = Interest rate per period (decimal)
n = Number of periods
PMT = Payment per period
For an annuity due (payments at the beginning of the period), the formula is slightly modified:
The calculator solves for any one of these variables (PV, FV, PMT, N, I/Y) when the others are provided. The logic involves rearranging the TVM formula or using iterative methods, especially for solving 'N' and 'I/Y'.
Common Use Cases:
Loan Analysis: Calculating loan payments, total interest paid, or the number of payments needed.
Investment Planning: Determining the future value of savings, the required down payment, or the interest rate needed to reach a financial goal.
Retirement Planning: Estimating the amount needed for retirement or the regular contributions required.
Lease vs. Buy Decisions: Comparing the total costs of financing options.
The TI BA II Plus Professional calculator streamlines these complex computations, providing accurate results quickly. This web-based simulator replicates its core TVM functionality for educational and practical purposes.
function getNumber(id) {
var value = parseFloat(document.getElementById(id).value);
return isNaN(value) ? 0 : value;
}
function getPaymentTiming() {
return parseInt(document.getElementById("paymentTiming").value);
}
function getPaymentFreq() {
return parseInt(document.getElementById("paymentFreq").value);
}
function calculatePV() {
var fv = getNumber("futureValue");
var pmt = getNumber("payment");
var n = getNumber("numPeriods");
var iy = getNumber("interestRate");
var freq = getPaymentFreq();
var timing = getPaymentTiming();
if (n === 0 || iy === 0) {
document.getElementById("result").innerHTML = "Error: N and I/Y cannot be zero for PV calculation.";
return;
}
var i = (iy / 100) / freq; // Interest rate per period
var numPeriodsAdjusted = n * freq; // Total periods if N is annual
var pv;
if (timing === 1) { // Annuity Due
pv = fv / Math.pow(1 + i, numPeriodsAdjusted) – pmt * (1 + i) * (1 – Math.pow(1 + i, numPeriodsAdjusted)) / i;
} else { // Ordinary Annuity
pv = fv / Math.pow(1 + i, numPeriodsAdjusted) – pmt * (1 – Math.pow(1 + i, numPeriodsAdjusted)) / i;
}
// Handle case where PMT is zero (simple compounding)
if (pmt === 0) {
pv = fv / Math.pow(1 + i, numPeriodsAdjusted);
}
document.getElementById("result").innerHTML = "Calculated PV: " + pv.toFixed(2) + "(Present Value)";
}
function calculateFV() {
var pv = getNumber("presentValue");
var pmt = getNumber("payment");
var n = getNumber("numPeriods");
var iy = getNumber("interestRate");
var freq = getPaymentFreq();
var timing = getPaymentTiming();
if (n === 0) {
document.getElementById("result").innerHTML = "Error: Number of Periods (N) cannot be zero for FV calculation.";
return;
}
var i = (iy / 100) / freq; // Interest rate per period
var numPeriodsAdjusted = n * freq; // Total periods if N is annual
var fv;
if (timing === 1) { // Annuity Due
fv = pv * Math.pow(1 + i, numPeriodsAdjusted) + pmt * (1 + i) * (Math.pow(1 + i, numPeriodsAdjusted) – 1) / i;
} else { // Ordinary Annuity
fv = pv * Math.pow(1 + i, numPeriodsAdjusted) + pmt * (Math.pow(1 + i, numPeriodsAdjusted) – 1) / i;
}
// Handle case where PMT is zero (simple compounding)
if (pmt === 0) {
fv = pv * Math.pow(1 + i, numPeriodsAdjusted);
}
document.getElementById("result").innerHTML = "Calculated FV: " + fv.toFixed(2) + "(Future Value)";
}
function calculatePMT() {
var pv = getNumber("presentValue");
var fv = getNumber("futureValue");
var n = getNumber("numPeriods");
var iy = getNumber("interestRate");
var freq = getPaymentFreq();
var timing = getPaymentTiming();
if (n === 0 || iy === 0) {
document.getElementById("result").innerHTML = "Error: N and I/Y cannot be zero for PMT calculation.";
return;
}
var i = (iy / 100) / freq; // Interest rate per period
var numPeriodsAdjusted = n * freq; // Total periods if N is annual
var pmt;
if (timing === 1) { // Annuity Due
pmt = (fv – pv * Math.pow(1 + i, numPeriodsAdjusted)) / ((1 + i) * (Math.pow(1 + i, numPeriodsAdjusted) – 1) / i);
} else { // Ordinary Annuity
pmt = (fv – pv * Math.pow(1 + i, numPeriodsAdjusted)) / ((Math.pow(1 + i, numPeriodsAdjusted) – 1) / i);
}
// Handle case where PV and FV are zero (solving for payment in a stream)
if (pv === 0 && fv === 0) {
// This case is ambiguous without more context, typically requires one of PV or FV to be non-zero.
document.getElementById("result").innerHTML = "Error: Cannot calculate PMT with both PV and FV as zero without additional context.";
return;
}
document.getElementById("result").innerHTML = "Calculated PMT: " + pmt.toFixed(2) + "(Payment per Period)";
}
function calculateN() {
var pv = getNumber("presentValue");
var fv = getNumber("futureValue");
var pmt = getNumber("payment");
var iy = getNumber("interestRate");
var freq = getPaymentFreq();
var timing = getPaymentTiming();
if (iy === 0) {
document.getElementById("result").innerHTML = "Error: Interest Rate (I/Y) cannot be zero for N calculation unless PV=FV and PMT=0.";
return;
}
if (pv === 0 && fv === 0 && pmt === 0) {
document.getElementById("result").innerHTML = "Error: Cannot calculate N with PV, FV, and PMT all zero.";
return;
}
var i = (iy / 100) / freq; // Interest rate per period
var n_periods;
// Formulas derived from TVM equation, solving for n. Requires logarithms.
// Different formulas for Annuity Due vs Ordinary Annuity and when PMT is zero.
if (pmt === 0) {
if (pv === 0) {
document.getElementById("result").innerHTML = "Error: Cannot solve for N when PV and PMT are zero.";
return;
}
// FV = PV * (1 + i)^n => n = log(FV/PV) / log(1+i)
n_periods = Math.log(fv / pv) / Math.log(1 + i);
} else if (timing === 1) { // Annuity Due
// FV = PV * (1 + i)^n + PMT * (1 + i) * [(1 + i)^n – 1] / i
// Rearranged: n = -log(1 – (i * (FV – PV*(1+i)^n)) / (PMT*(1+i))) / log(1+i)
// This requires iteration or a numerical solver in a real calculator for precision.
// A simplified approach or approximation might be needed for direct JS implementation,
// or we use the formula derived from the annuity part:
// FV_annuity_due = PMT * (1+i) * [(1+i)^n – 1] / i
// var FV_adjusted = FV – PV * (1 + i)^n (This is problematic as n is unknown)
// Instead, we use: (FV – PV*(1+i)^n) / (PMT*(1+i)) = [(1+i)^n – 1] / i
// i * (FV – PV*(1+i)^n) / (PMT*(1+i)) = (1+i)^n – 1
// 1 + i * (FV – PV*(1+i)^n) / (PMT*(1+i)) = (1+i)^n
// log(1 + i * (FV – PV*(1+i)^n) / (PMT*(1+i))) / log(1+i) = n
// This is still circular. The standard approach uses numerical methods or direct formula rearrangement.
// Let's rearrange the standard FV formula:
// FV = PV(1+i)^n + PMT[(1+i)^n – 1]/i (Ordinary)
// FV = PV(1+i)^n + PMT(1+i)[(1+i)^n – 1]/i (Due)
// For Annuity Due:
// FV / (1+i) = PV(1+i)^(n-1) + PMT[(1+i)^n – 1]/i
// var FV' = FV / (1+i)
// FV' = PV(1+i)^n + PMT[(1+i)^n – 1]/i — This is not quite right.
// Correct Rearrangement for Annuity Due to solve for N:
// FV = PV * (1 + i)^n + PMT * (1 + i) * ( (1 + i)^n – 1 ) / i
// var X = (1+i)^n
// FV = PV * X + PMT * (1 + i) * (X – 1) / i
// FV * i / (PMT * (1 + i)) = (X – 1) * i / (PMT * (1 + i)) + PV * X * i / (PMT * (1 + i))
// FV * i / (PMT * (1 + i)) = (X – 1) + PV * X * i / (PMT * (1 + i))
// var A = FV * i / (PMT * (1 + i))
// var B = PV * i / (PMT * (1 + i))
// A = X – 1 + B * X
// A + 1 = X * (1 + B)
// X = (A + 1) / (1 + B)
// (1 + i)^n = ( (FV * i / (PMT * (1 + i))) + 1 ) / ( 1 + (PV * i / (PMT * (1 + i))) )
// n = log [ ( (FV * i / (PMT * (1 + i))) + 1 ) / ( 1 + (PV * i / (PMT * (1 + i))) ) ] / log(1 + i)
var term1 = (fv * i) / (pmt * (1 + i));
var term2 = (pv * i) / (pmt * (1 + i));
n_periods = Math.log(term1 + 1) – Math.log(1 + term2) / Math.log(1 + i);
} else { // Ordinary Annuity
// FV = PV * (1 + i)^n + PMT * [ (1 + i)^n – 1 ] / i
// Rearranging to solve for n:
// (FV – PV * (1 + i)^n) = PMT * [ (1 + i)^n – 1 ] / i
// i * (FV – PV * (1 + i)^n) / PMT = (1 + i)^n – 1
// 1 + i * (FV – PV * (1 + i)^n) / PMT = (1 + i)^n
// var X = (1+i)^n
// 1 + i * (FV – PV * X) / PMT = X
// var A = i / PMT
// 1 + A * (FV – PV * X) = X
// 1 + A * FV – A * PV * X = X
// 1 + A * FV = X * (1 + A * PV)
// X = (1 + A * FV) / (1 + A * PV)
// (1 + i)^n = (1 + (i/PMT) * FV) / (1 + (i/PMT) * PV)
// n = log [ (1 + i * FV / PMT) / (1 + i * PV / PMT) ] / log(1 + i)
n_periods = Math.log(1 + (i * fv) / pmt) – Math.log(1 + (i * pv) / pmt) / Math.log(1 + i);
}
var n_years = n_periods / freq; // Convert back to years if freq > 1
document.getElementById("result").innerHTML = "Calculated N: " + n_periods.toFixed(2) + " periods(Approximately " + n_years.toFixed(2) + " years)";
}
function calculateI() {
var pv = getNumber("presentValue");
var fv = getNumber("futureValue");
var pmt = getNumber("payment");
var n = getNumber("numPeriods");
var freq = getPaymentFreq();
var timing = getPaymentTiming();
if (n === 0 || pv === 0) {
document.getElementById("result").innerHTML = "Error: N and PV cannot be zero for I/Y calculation.";
return;
}
var numPeriodsAdjusted = n * freq;
var i = 0; // Initial guess for interest rate per period
var error = 0.00001; // Tolerance for convergence
var maxIterations = 1000; // Prevent infinite loops
var step = 0.0001; // Step for numerical search
// Newton-Raphson method or bisection method is typically used.
// For simplicity here, we'll use a simpler iterative approach trying small increments.
// A more robust solution would involve Newton-Raphson.
var low = 0.00001; // Lower bound for interest rate (avoid division by zero)
var high = 2.0; // Upper bound for interest rate (200%)
// Bisection method for finding root of f(i) = 0
var func = function(rate) {
var term_pv = pv * Math.pow(1 + rate, numPeriodsAdjusted);
var term_pmt;
if (pmt === 0) {
term_pmt = 0;
} else if (timing === 1) { // Annuity Due
term_pmt = pmt * (1 + rate) * (Math.pow(1 + rate, numPeriodsAdjusted) – 1) / rate;
} else { // Ordinary Annuity
term_pmt = pmt * (Math.pow(1 + rate, numPeriodsAdjusted) – 1) / rate;
}
return term_pv + term_pmt – fv;
};
var rate = 0;
for (var iter = 0; iter < maxIterations; iter++) {
rate = (high + low) / 2;
var func_val = func(rate);
if (Math.abs(func_val) 0) {
high = rate; // Root is in the lower half
} else {
low = rate; // Root is in the upper half
}
if (iter === maxIterations – 1) {
document.getElementById("result").innerHTML = "Error: Could not converge to an interest rate within " + maxIterations + " iterations.";
return;
}
}
var iy = rate * 100 * freq; // Convert rate per period back to annual percentage rate
document.getElementById("result").innerHTML = "Calculated I/Y: " + iy.toFixed(2) + "%(Interest Rate per Year)";
}
function clearFields() {
document.getElementById("presentValue").value = "";
document.getElementById("futureValue").value = "";
document.getElementById("payment").value = "";
document.getElementById("numPeriods").value = "";
document.getElementById("interestRate").value = "";
document.getElementById("paymentFreq").value = 1; // Reset to default
document.getElementById("paymentTiming").value = 0; // Reset to default
document.getElementById("result").innerHTML = "Enter values and click a calculation button.";
}