This calculator emulates the core Time Value of Money (TVM) functions of a TI BA II Plus financial calculator. Input four of the five TVM variables (N, I/Y, PV, PMT, FV) and leave one blank to solve for the unknown. Remember to use the correct cash flow signs!
Understanding the TI BA II Plus Financial Calculator
The TI BA II Plus is a popular financial calculator used by students and professionals for various financial calculations, particularly those involving the Time Value of Money (TVM). This online tool replicates its core TVM functionality, allowing you to solve for one unknown variable when the others are known.
Key TVM Variables:
N (Number of Periods): The total number of compounding or payment periods. For a 30-year loan with monthly payments, N would be 360 (30 * 12).
I/Y (Annual Interest Rate %): The nominal annual interest rate. This is entered as a percentage (e.g., 5 for 5%).
PV (Present Value): The current value of a future sum of money or stream of cash flows. This is often the principal amount of a loan or an initial investment.
PMT (Payment Amount): The amount of each regular payment or deposit.
FV (Future Value): The value of an asset or cash at a specified date in the future. For a fully amortized loan, FV is typically 0.
Important Settings:
P/Y (Payments Per Year): The number of payments made in a year (e.g., 12 for monthly, 1 for annually).
C/Y (Compounding Periods Per Year): The number of times interest is compounded in a year. Often, P/Y and C/Y are the same. If they differ, the calculator adjusts the interest rate accordingly.
Payment Timing (End/Beginning): Specifies whether payments occur at the end (ordinary annuity) or beginning (annuity due) of each period.
Cash Flow Signs:
A critical aspect of using financial calculators like the TI BA II Plus is understanding cash flow signs:
Cash Inflows are Positive: Money you receive (e.g., a loan principal, a future investment payout).
Cash Outflows are Negative: Money you pay out (e.g., loan payments, initial investment, regular deposits).
For example, if you take out a $100,000 loan, PV would be 100000. Your monthly payments would be entered as a negative number, e.g., -536.82. If you are saving for retirement, your initial investment (PV) and regular deposits (PMT) would be negative, and your future value (FV) would be positive.
Example Scenarios:
Calculating Loan Payment (Solve for PMT):
N: 360 (30 years * 12 months)
I/Y: 5 (%)
PV: 100000 (Loan amount received)
FV: 0 (Loan paid off)
P/Y: 12, C/Y: 12, Payment Timing: End
Result: PMT ≈ -536.82 (Monthly payment outflow)
Future Value of an Investment (Solve for FV):
N: 120 (10 years * 12 months)
I/Y: 8 (%)
PV: -10000 (Initial investment paid)
PMT: -100 (Monthly deposit paid)
P/Y: 12, C/Y: 12, Payment Timing: End
Result: FV ≈ 30,000 – 40,000 (Future value received)
Number of Payments to Pay Off a Loan (Solve for N):
I/Y: 6 (%)
PV: 50000 (Loan amount received)
PMT: -500 (Monthly payment outflow)
FV: 0 (Loan paid off)
P/Y: 12, C/Y: 12, Payment Timing: End
Result: N ≈ 120-130 periods
function calculateTVM() {
var nPeriodsStr = document.getElementById("nPeriods").value;
var annualRateStr = document.getElementById("annualRate").value;
var presentValueStr = document.getElementById("presentValue").value;
var paymentAmountStr = document.getElementById("paymentAmount").value;
var futureValueStr = document.getElementById("futureValue").value;
var paymentsPerYearStr = document.getElementById("paymentsPerYear").value;
var compoundingPerYearStr = document.getElementById("compoundingPerYear").value;
var paymentTiming = document.querySelector('input[name="paymentTiming"]:checked').value;
var nPeriods = parseFloat(nPeriodsStr);
var annualRate = parseFloat(annualRateStr);
var presentValue = parseFloat(presentValueStr);
var paymentAmount = parseFloat(paymentAmountStr);
var futureValue = parseFloat(futureValueStr);
var paymentsPerYear = parseFloat(paymentsPerYearStr);
var compoundingPerYear = parseFloat(compoundingPerYearStr);
var blankCount = 0;
var blankField = "";
if (isNaN(nPeriods)) { blankCount++; blankField = "N"; }
if (isNaN(annualRate)) { blankCount++; blankField = "I/Y"; }
if (isNaN(presentValue)) { blankCount++; blankField = "PV"; }
if (isNaN(paymentAmount)) { blankCount++; blankField = "PMT"; }
if (isNaN(futureValue)) { blankCount++; blankField = "FV"; }
if (blankCount !== 1) {
document.getElementById("result").innerHTML = "Please leave exactly one field blank to solve for.";
return;
}
if (isNaN(paymentsPerYear) || paymentsPerYear <= 0) {
paymentsPerYear = 12; // Default
document.getElementById("paymentsPerYear").value = 12;
}
if (isNaN(compoundingPerYear) || compoundingPerYear <= 0) {
compoundingPerYear = 12; // Default
document.getElementById("compoundingPerYear").value = 12;
}
var result = "";
var i_effective_payment_period; // Rate per payment period
// Calculate effective periodic rate based on P/Y and C/Y
if (paymentsPerYear === compoundingPerYear) {
i_effective_payment_period = (annualRate / 100) / paymentsPerYear;
} else {
// Convert annual rate compounded C/Y times to an effective rate for P/Y periods
var effectiveAnnualRate = Math.pow(1 + (annualRate / 100) / compoundingPerYear, compoundingPerYear) – 1;
i_effective_payment_period = Math.pow(1 + effectiveAnnualRate, 1 / paymentsPerYear) – 1;
}
var i = i_effective_payment_period; // Use this 'i' for TVM formulas
var n = nPeriods; // Total number of payment periods
var adj = (paymentTiming === 'beginning' ? (1 + i) : 1);
// Define a small tolerance for floating point comparisons and zero rate
var tolerance = 0.00000001;
var maxIterations = 1000;
// Function to evaluate the TVM equation: PV*(1+i)^N + PMT*(((1+i)^N-1)/i)*adj + FV = 0
function evaluateTVM(current_i, current_n, pv, pmt, fv, current_adj) {
if (Math.abs(current_i) < tolerance) { // Handle zero interest rate
return pv + pmt * current_n * 1 + fv; // adj becomes 1 for i=0
}
var term1 = Math.pow(1 + current_i, current_n);
var term2 = (term1 – 1) / current_i;
return pv * term1 + pmt * term2 * current_adj + fv;
}
// Handle zero interest rate for direct calculations
if (Math.abs(i) < tolerance && blankField !== "I/Y") {
adj = 1; // For i=0, (1+i) is 1, so adj is always 1.
if (blankField === "FV") {
result = -presentValue – paymentAmount * n * adj;
} else if (blankField === "PV") {
result = -futureValue – paymentAmount * n * adj;
} else if (blankField === "PMT") {
if (n === 0) { result = NaN; }
else { result = (-presentValue – futureValue) / (n * adj); }
} else if (blankField === "N") {
if (paymentAmount === 0) { result = NaN; }
else { result = (-presentValue – futureValue) / (paymentAmount * adj); }
}
} else { // Non-zero interest rate or solving for I/Y
var term1 = Math.pow(1 + i, n);
var term2 = (term1 – 1) / i;
if (blankField === "FV") {
result = -presentValue * term1 – paymentAmount * term2 * adj;
} else if (blankField === "PV") {
result = (-futureValue – paymentAmount * term2 * adj) / term1;
} else if (blankField === "PMT") {
if (Math.abs(term2 * adj) < tolerance) { result = NaN; } // Avoid division by zero
else { result = (-presentValue * term1 – futureValue) / (term2 * adj); }
} else if (blankField === "N") {
// Numerical solver for N
var lowN = 0.0000001;
var highN = 100000; // Max periods, e.g., 8333 years of monthly payments
var solvedN = NaN;
for (var iterN = 0; iterN < maxIterations; iterN++) {
var midN = (lowN + highN) / 2;
if (midN <= 0) { // N must be positive
lowN = 0.0000001;
continue;
}
var f_midN = evaluateTVM(i, midN, presentValue, paymentAmount, futureValue, adj);
if (Math.abs(f_midN) 0, it means we need a higher N to bring it down to 0.
if (f_midN > 0) {
lowN = midN;
} else {
highN = midN;
}
}
result = solvedN;
} else if (blankField === "I/Y") {
// Numerical solver for I/Y (periodic rate)
var lowRate = 0.0000001; // 0.00001% periodic rate
var highRate = 1.0; // 100% periodic rate
var solvedPeriodicRate = NaN;
for (var iterRate = 0; iterRate < maxIterations; iterRate++) {
var midRate = (lowRate + highRate) / 2;
if (midRate === 0) { // Avoid division by zero in evaluateTVM if rate is exactly 0
lowRate = midRate;
continue;
}
var currentAdjRate = (paymentTiming === 'beginning' ? (1 + midRate) : 1);
var f_midRate = evaluateTVM(midRate, n, presentValue, paymentAmount, futureValue, currentAdjRate);
if (Math.abs(f_midRate) 0, it means the current midRate is too low, and we need a higher rate.
if (f_midRate > 0) {
lowRate = midRate;
} else {
highRate = midRate;
}
}
if (!isNaN(solvedPeriodicRate)) {
// Convert periodic rate to annual percentage based on P/Y
result = solvedPeriodicRate * paymentsPerYear * 100;
} else {
result = NaN;
}
}
}
if (isNaN(result) || !isFinite(result)) {
document.getElementById("result").innerHTML = "Cannot calculate. Please check your inputs, cash flow signs, or if a solution exists.";
} else {
var formattedResult = result.toFixed(2);
var unit = "";
if (blankField === "I/Y") { unit = "%"; }
else if (blankField === "N") { unit = " periods"; }
// PV, PMT, FV are amounts, no specific unit here, user defines currency context.
document.getElementById("result").innerHTML = "" + blankField + " = " + formattedResult + unit + "";
// Update the blank field with the calculated value
if (blankField === "N") { document.getElementById("nPeriods").value = formattedResult; }
else if (blankField === "I/Y") { document.getElementById("annualRate").value = formattedResult; }
else if (blankField === "PV") { document.getElementById("presentValue").value = formattedResult; }
else if (blankField === "PMT") { document.getElementById("paymentAmount").value = formattedResult; }
else if (blankField === "FV") { document.getElementById("futureValue").value = formattedResult; }
}
}
function clearFields() {
document.getElementById("nPeriods").value = "";
document.getElementById("annualRate").value = "";
document.getElementById("presentValue").value = "";
document.getElementById("paymentAmount").value = "";
document.getElementById("futureValue").value = "";
document.getElementById("paymentsPerYear").value = "12";
document.getElementById("compoundingPerYear").value = "12";
document.getElementById("paymentTimingEnd").checked = true;
document.getElementById("result").innerHTML = "";
}