Rate Function

Returns a Double specifying the interest rate per period for an annuity.

Syntax

Rate(nper, pmt, pv, [fv], [type], [guess])

Parameters

• nper - Required. Double specifying total number of payment periods in the annuity. For example, if you make monthly payments on a 4-year car loan, your loan has 4 * 12 (or 48) payment periods.
• pmt - Required. Double specifying payment to be made each period. Payments usually contain principal and interest that doesn't change over the life of the annuity.
• pv - Required. Double specifying present value, or value today, of a series of future payments or receipts. For example, when you borrow money to buy a car, the loan amount is the present value to the lender of the monthly car payments you will make.
• fv - Optional. Variant specifying future value or cash balance you want after you've made the final payment. For example, the future value of a loan is $0 because that's its value after the final payment. However, if you want to save $50,000 over 18 years for your child's education, then $50,000 is the future value. If omitted, 0 is assumed.
• type - Optional. Variant specifying when payments are due. Use 0 if payments are due at the end of the payment period, or use 1 if payments are due at the beginning of the period. If omitted, 0 is assumed.
• guess - Optional. Variant specifying value you estimate will be returned by Rate. If omitted, guess is 0.1 (10 percent). Rate is calculated by iteration and can have zero or more than one solution.

Return Value

Returns a Double specifying the interest rate per period for an annuity. The rate is calculated using an iterative algorithm and is returned as a decimal (e.g., 0.08 for 8%).

Remarks

The Rate function calculates the interest rate per period for an annuity based on periodic, fixed payments and a fixed principal. This is useful when you know the loan amount, payment, and term, but need to determine what interest rate is being charged. An annuity is a series of fixed cash payments made over a period of time. An annuity can be a loan (such as a home mortgage) or an investment (such as a monthly savings plan). For all arguments, cash paid out (such as deposits to savings) is represented by negative numbers; cash received (such as dividend checks) is represented by positive numbers. Important Notes: - The Rate function uses an iterative technique to calculate the interest rate - If Rate cannot find a result after 20 iterations, it fails and returns an error - Different values for guess can result in different solutions or no solution - The rate returned is per period - multiply by periods per year for annual rate - Be consistent with units: if nper is in months, the result is monthly rate Calculation Method: The Rate function solves the present value equation for the rate:

PV + PMT * ((1 - (1 + rate)^-nper) / rate) + FV / (1 + rate)^nper = 0

Typical Uses

1. Loan Analysis: Determine the interest rate on a loan given payment and terms
2. APR Calculation: Calculate Annual Percentage Rate from payment information
3. Investment Returns: Find the rate of return on an investment
4. Lease Rate Discovery: Determine implicit interest rate in a lease
5. Loan Comparison: Compare effective rates between different loan offers
6. Reverse Engineering: Find the rate when only payment details are known
7. Financial Planning: Calculate required rate of return for goals
8. Credit Card Analysis: Determine effective rate from minimum payments

Basic Examples

Example 1: Find Loan Interest Rate

' You borrowed $10,000, pay $200/month for 5 years. What's the monthly rate?
Dim monthlyRate As Double
Dim annualRate As Double
monthlyRate = Rate(60, -200, 10000)
annualRate = monthlyRate * 12
' monthlyRate ≈ 0.00618 (0.618% per month)
' annualRate ≈ 0.0742 (7.42% APR)

Example 2: Investment Rate of Return

' Invested $5,000, withdrew $100/month for 5 years, ended with $3,000. What was the rate?
Dim monthlyReturn As Double
monthlyReturn = Rate(60, 100, -5000, 3000)
' Returns the monthly rate of return

Example 3: Find Rate with Guess

' Sometimes need to provide a guess to help convergence
Dim rate As Double
rate = Rate(48, -250, 10000, 0, 0, 0.08)  ' Guess 8% annual (0.08/12 monthly)

Example 4: Annual Rate from Monthly Terms

' Calculate APR from monthly payment information
Dim monthlyRate As Double
Dim apr As Double
monthlyRate = Rate(360, -1000, 150000)  ' 30-year mortgage
apr = monthlyRate * 12 * 100  ' Convert to annual percentage
MsgBox "APR: " & Format(apr, "0.00") & "%"

Common Patterns

Pattern 1: CalculateAPR

Function CalculateAPR(loanAmount As Double, monthlyPayment As Double, _
                      months As Integer) As Double
    ' Calculate Annual Percentage Rate from loan terms
    Dim monthlyRate As Double
    On Error Resume Next
    monthlyRate = Rate(months, -monthlyPayment, loanAmount)
    If Err.Number = 0 Then
        CalculateAPR = monthlyRate * 12  ' Convert to annual rate
    Else
        CalculateAPR = -1  ' Error indicator
        Err.Clear
    End If
    On Error GoTo 0
End Function

Pattern 2: CompareEffectiveRates

Function CompareEffectiveRates(loan1PV As Double, loan1PMT As Double, loan1Nper As Integer, _
                               loan2PV As Double, loan2PMT As Double, loan2Nper As Integer) As String
    Dim rate1 As Double, rate2 As Double
    On Error Resume Next
    rate1 = Rate(loan1Nper, -loan1PMT, loan1PV) * 12
    rate2 = Rate(loan2Nper, -loan2PMT, loan2PV) * 12
    If Err.Number <> 0 Then
        CompareEffectiveRates = "Error calculating rates"
        Err.Clear
        Exit Function
    End If
    On Error GoTo 0
    If rate1 < rate2 Then
        CompareEffectiveRates = "Loan 1 has lower rate: " & Format(rate1 * 100, "0.00") & "%"
    ElseIf rate2 < rate1 Then
        CompareEffectiveRates = "Loan 2 has lower rate: " & Format(rate2 * 100, "0.00") & "%"
    Else
        CompareEffectiveRates = "Both loans have same rate: " & Format(rate1 * 100, "0.00") & "%"
    End If
End Function

Pattern 3: ValidateRateParameters

Function ValidateRateParameters(nper As Integer, pmt As Double, pv As Double) As Boolean
    ValidateRateParameters = False
    If nper <= 0 Then
        MsgBox "Number of periods must be positive"
        Exit Function
    End If
    If pmt = 0 Then
        MsgBox "Payment cannot be zero"
        Exit Function
    End If
    If pv = 0 Then
        MsgBox "Present value cannot be zero"
        Exit Function
    End If
    ' Check if payment and PV have proper sign relationship
    If (pmt > 0 And pv > 0) Or (pmt < 0 And pv < 0) Then
        MsgBox "Payment and present value must have opposite signs"
        Exit Function
    End If
    ValidateRateParameters = True
End Function

Pattern 4: FindRateWithRetry

Function FindRateWithRetry(nper As Integer, pmt As Double, pv As Double, _
                           Optional fv As Double = 0) As Double
    ' Try multiple guess values if initial attempt fails
    Dim guesses As Variant
    Dim i As Integer
    Dim rate As Double
    guesses = Array(0.1, 0.05, 0.15, 0.01, 0.2, 0.001)
    For i = LBound(guesses) To UBound(guesses)
        On Error Resume Next
        rate = Rate(nper, pmt, pv, fv, 0, guesses(i))
        If Err.Number = 0 Then
            FindRateWithRetry = rate
            Exit Function
        End If
        Err.Clear
    Next i
    On Error GoTo 0
    FindRateWithRetry = -999  ' Error code
End Function

Pattern 5: CalculateEffectiveAPR

Function CalculateEffectiveAPR(loanAmount As Double, payment As Double, _
                               years As Integer, fees As Double) As Double
    ' Calculate APR including fees
    Dim months As Integer
    Dim netLoanAmount As Double
    Dim monthlyRate As Double
    months = years * 12
    netLoanAmount = loanAmount - fees  ' Reduce by fees paid upfront
    monthlyRate = Rate(months, -payment, netLoanAmount)
    CalculateEffectiveAPR = monthlyRate * 12
End Function

Pattern 6: GetLeaseImplicitRate

Function GetLeaseImplicitRate(vehiclePrice As Double, monthlyPayment As Double, _
                              leaseTerm As Integer, residualValue As Double) As Double
    ' Find the implicit interest rate in a lease
    Dim monthlyRate As Double
    ' For a lease, the PV is the vehicle price, FV is the residual value
    monthlyRate = Rate(leaseTerm, -monthlyPayment, vehiclePrice, -residualValue)
    GetLeaseImplicitRate = monthlyRate * 12  ' Annual rate
End Function

Pattern 7: CalculateRealRate

Function CalculateRealRate(nper As Integer, pmt As Double, pv As Double, _
                           inflationRate As Double) As Double
    ' Calculate real (inflation-adjusted) rate of return
    Dim nominalRate As Double
    Dim realRate As Double
    nominalRate = Rate(nper, pmt, pv)
    ' Fisher equation: (1 + nominal) = (1 + real)(1 + inflation)
    realRate = ((1 + nominalRate) / (1 + inflationRate / 12)) - 1
    CalculateRealRate = realRate
End Function

Pattern 8: ConvertToAPY

Function ConvertToAPY(periodicRate As Double, periodsPerYear As Integer) As Double
    ' Convert periodic rate to Annual Percentage Yield (with compounding)
    ConvertToAPY = ((1 + periodicRate) ^ periodsPerYear) - 1
End Function

Pattern 9: BackoutRate

Function BackoutRate(payment As Double, principal As Double, _
                     years As Integer, paymentType As Integer) As Double
    ' Reverse engineer the rate from payment information
    Dim periods As Integer
    Dim rate As Double
    periods = years * 12
    On Error Resume Next
    rate = Rate(periods, -payment, principal, 0, paymentType)
    If Err.Number = 0 Then
        BackoutRate = rate * 12  ' Annual rate
    Else
        BackoutRate = -1
        Err.Clear
    End If
    On Error GoTo 0
End Function

Pattern 10: IsRateReasonable

Function IsRateReasonable(calculatedRate As Double) As Boolean
    ' Validate that calculated rate is within reasonable bounds
    Dim annualRate As Double
    annualRate = calculatedRate * 12
    ' Check if annual rate is between -50% and +50%
    IsRateReasonable = (annualRate >= -0.5 And annualRate <= 0.5)
End Function

Advanced Usage

Example 1: Comprehensive Loan Rate Analyzer

' Analyze and compare loan rates with detailed calculations
Class LoanRateAnalyzer
    Private m_loanAmount As Double
    Private m_monthlyPayment As Double
    Private m_numPayments As Integer
    Private m_fees As Double
    Private m_calculatedRate As Double
    Private m_effectiveRate As Double
    Public Sub Initialize(loanAmount As Double, monthlyPayment As Double, _
                         years As Integer, Optional fees As Double = 0)
        m_loanAmount = loanAmount
        m_monthlyPayment = monthlyPayment
        m_numPayments = years * 12
        m_fees = fees
    End Sub
    Public Function CalculateNominalRate() As Double
        ' Calculate the stated interest rate
        Dim monthlyRate As Double
        On Error Resume Next
        monthlyRate = Rate(m_numPayments, -m_monthlyPayment, m_loanAmount)
        If Err.Number = 0 Then
            m_calculatedRate = monthlyRate * 12
            CalculateNominalRate = m_calculatedRate
        Else
            CalculateNominalRate = -1
            Err.Clear
        End If
        On Error GoTo 0
    End Function
    Public Function CalculateEffectiveRate() As Double
        ' Calculate APR including fees
        Dim netAmount As Double
        Dim monthlyRate As Double
        netAmount = m_loanAmount - m_fees
        On Error Resume Next
        monthlyRate = Rate(m_numPayments, -m_monthlyPayment, netAmount)
        If Err.Number = 0 Then
            m_effectiveRate = monthlyRate * 12
            CalculateEffectiveRate = m_effectiveRate
        Else
            CalculateEffectiveRate = -1
            Err.Clear
        End If
        On Error GoTo 0
    End Function
    Public Function CalculateAPY() As Double
        ' Calculate Annual Percentage Yield (with compounding)
        Dim monthlyRate As Double
        monthlyRate = m_calculatedRate / 12
        CalculateAPY = ((1 + monthlyRate) ^ 12) - 1
    End Function
    Public Function GetTotalInterestPaid() As Double
        ' Calculate total interest over life of loan
        GetTotalInterestPaid = (m_monthlyPayment * m_numPayments) - m_loanAmount
    End Function
    Public Function GetInterestPercentage() As Double
        ' Calculate interest as percentage of principal
        GetInterestPercentage = GetTotalInterestPaid() / m_loanAmount
    End Function
    Public Function GenerateRateReport() As String
        Dim report As String
        Dim nominalRate As Double
        Dim effectiveRate As Double
        Dim apy As Double
        nominalRate = CalculateNominalRate()
        effectiveRate = CalculateEffectiveRate()
        If nominalRate < 0 Or effectiveRate < 0 Then
            GenerateRateReport = "Error: Could not calculate interest rate"
            Exit Function
        End If
        apy = CalculateAPY()
        report = "Loan Rate Analysis" & vbCrLf
        report = report & String(50, "=") & vbCrLf
        report = report & "Loan Amount: $" & Format(m_loanAmount, "#,##0.00") & vbCrLf
        report = report & "Monthly Payment: $" & Format(m_monthlyPayment, "#,##0.00") & vbCrLf
        report = report & "Term: " & (m_numPayments / 12) & " years (" & m_numPayments & " months)" & vbCrLf
        report = report & "Fees: $" & Format(m_fees, "#,##0.00") & vbCrLf
        report = report & String(50, "-") & vbCrLf
        report = report & "Nominal APR: " & Format(nominalRate * 100, "0.00") & "%" & vbCrLf
        report = report & "Effective APR (with fees): " & Format(effectiveRate * 100, "0.00") & "%" & vbCrLf
        report = report & "APY (with compounding): " & Format(apy * 100, "0.00") & "%" & vbCrLf
        report = report & String(50, "-") & vbCrLf
        report = report & "Total Interest Paid: $" & Format(GetTotalInterestPaid(), "#,##0.00") & vbCrLf
        report = report & "Interest as % of Principal: " & Format(GetInterestPercentage() * 100, "0.00") & "%"
        GenerateRateReport = report
    End Function
End Class

Example 2: Multi-Loan Rate Comparison Tool

' Compare rates across multiple loan offers
Module LoanRateComparison
    Private Type LoanOffer
        Name As String
        Principal As Double
        Payment As Double
        Months As Integer
        Fees As Double
        NominalRate As Double
        EffectiveRate As Double
    End Type
    Public Function CompareLoans(offers() As LoanOffer) As String
        Dim i As Integer
        Dim report As String
        Dim bestOffer As Integer
        Dim lowestRate As Double
        lowestRate = 999
        bestOffer = LBound(offers)
        ' Calculate rates for all offers
        For i = LBound(offers) To UBound(offers)
            With offers(i)
                On Error Resume Next
                .NominalRate = Rate(.Months, -.Payment, .Principal) * 12
                .EffectiveRate = Rate(.Months, -.Payment, .Principal - .Fees) * 12
                If Err.Number <> 0 Then
                    .NominalRate = -1
                    .EffectiveRate = -1
                    Err.Clear
                End If
                On Error GoTo 0
                If .EffectiveRate > 0 And .EffectiveRate < lowestRate Then
                    lowestRate = .EffectiveRate
                    bestOffer = i
                End If
            End With
        Next i
        ' Generate comparison report
        report = "Loan Offer Comparison" & vbCrLf
        report = report & String(80, "=") & vbCrLf
        report = report & "Offer                Principal    Payment   Term   Fees      APR      Eff.APR" & vbCrLf
        report = report & String(80, "-") & vbCrLf
        For i = LBound(offers) To UBound(offers)
            With offers(i)
                report = report & Left(.Name & Space(20), 20)
                report = report & " $" & Right(Space(9) & Format(.Principal, "#,##0"), 9)
                report = report & "  $" & Right(Space(7) & Format(.Payment, "#,##0"), 7)
                report = report & Right(Space(5) & (.Months / 12), 5) & "y"
                report = report & " $" & Right(Space(6) & Format(.Fees, "#,##0"), 6)
                If .NominalRate >= 0 Then
                    report = report & Right(Space(6) & Format(.NominalRate * 100, "0.00"), 6) & "%"
                    report = report & Right(Space(7) & Format(.EffectiveRate * 100, "0.00"), 7) & "%"
                Else
                    report = report & "  Error   Error"
                End If
                If i = bestOffer Then report = report & " *BEST*"
                report = report & vbCrLf
            End With
        Next i
        report = report & String(80, "-") & vbCrLf
        report = report & "Best Offer: " & offers(bestOffer).Name & _
                 " (Effective APR: " & Format(offers(bestOffer).EffectiveRate * 100, "0.00") & "%)"
        CompareLoans = report
    End Function
    Public Function CalculateRateDifference(loan1 As LoanOffer, loan2 As LoanOffer) As String
        Dim diff As Double
        Dim savingsPerMonth As Double
        Dim totalSavings As Double
        diff = Abs(loan1.EffectiveRate - loan2.EffectiveRate)
        savingsPerMonth = Abs(loan1.Payment - loan2.Payment)
        totalSavings = savingsPerMonth * loan1.Months
        CalculateRateDifference = "Rate Difference: " & Format(diff * 100, "0.00") & "%" & vbCrLf & _
                                 "Monthly Savings: $" & Format(savingsPerMonth, "#,##0.00") & vbCrLf & _
                                 "Total Savings: $" & Format(totalSavings, "#,##0.00")
    End Function
End Module

Example 3: Investment Rate Calculator

' Calculate rate of return on investments
Class InvestmentRateCalculator
    Private m_initialInvestment As Double
    Private m_monthlyContribution As Double
    Private m_finalValue As Double
    Private m_months As Integer
    Public Sub Initialize(initialInvestment As Double, monthlyContribution As Double, _
                         finalValue As Double, years As Integer)
        m_initialInvestment = initialInvestment
        m_monthlyContribution = monthlyContribution
        m_finalValue = finalValue
        m_months = years * 12
    End Sub
    Public Function GetMonthlyRate() As Double
        ' Calculate monthly rate of return
        On Error Resume Next
        GetMonthlyRate = Rate(m_months, -m_monthlyContribution, -m_initialInvestment, m_finalValue)
        If Err.Number <> 0 Then
            GetMonthlyRate = -999
            Err.Clear
        End If
        On Error GoTo 0
    End Function
    Public Function GetAnnualRate() As Double
        Dim monthlyRate As Double
        monthlyRate = GetMonthlyRate()
        If monthlyRate = -999 Then
            GetAnnualRate = -999
        Else
            GetAnnualRate = monthlyRate * 12
        End If
    End Function
    Public Function GetEffectiveAnnualRate() As Double
        ' Calculate with compounding
        Dim monthlyRate As Double
        monthlyRate = GetMonthlyRate()
        If monthlyRate = -999 Then
            GetEffectiveAnnualRate = -999
        Else
            GetEffectiveAnnualRate = ((1 + monthlyRate) ^ 12) - 1
        End If
    End Function
    Public Function GetTotalContributed() As Double
        GetTotalContributed = m_initialInvestment + (m_monthlyContribution * m_months)
    End Function
    Public Function GetTotalReturn() As Double
        GetTotalReturn = m_finalValue - GetTotalContributed()
    End Function
    Public Function GenerateReport() As String
        Dim report As String
        Dim annualRate As Double
        Dim effectiveRate As Double
        annualRate = GetAnnualRate()
        effectiveRate = GetEffectiveAnnualRate()
        If annualRate = -999 Then
            GenerateReport = "Error: Could not calculate rate of return"
            Exit Function
        End If
        report = "Investment Rate of Return Analysis" & vbCrLf
        report = report & String(50, "=") & vbCrLf
        report = report & "Initial Investment: $" & Format(m_initialInvestment, "#,##0.00") & vbCrLf
        report = report & "Monthly Contribution: $" & Format(m_monthlyContribution, "#,##0.00") & vbCrLf
        report = report & "Investment Period: " & (m_months / 12) & " years" & vbCrLf
        report = report & "Final Value: $" & Format(m_finalValue, "#,##0.00") & vbCrLf
        report = report & String(50, "-") & vbCrLf
        report = report & "Total Contributed: $" & Format(GetTotalContributed(), "#,##0.00") & vbCrLf
        report = report & "Total Return: $" & Format(GetTotalReturn(), "#,##0.00") & vbCrLf
        report = report & String(50, "-") & vbCrLf
        report = report & "Annual Rate of Return: " & Format(annualRate * 100, "0.00") & "%" & vbCrLf
        report = report & "Effective Annual Rate: " & Format(effectiveRate * 100, "0.00") & "%"
        GenerateReport = report
    End Function
End Class

Example 4: Credit Card Rate Analyzer

' Analyze credit card interest rates from payment information
Class CreditCardRateAnalyzer
    Private m_balance As Double
    Private m_minimumPayment As Double
    Private m_monthsToPayoff As Integer
    Public Sub SetCardDetails(balance As Double, minimumPayment As Double, _
                             monthsToPayoff As Integer)
        m_balance = balance
        m_minimumPayment = minimumPayment
        m_monthsToPayoff = monthsToPayoff
    End Sub
    Public Function GetImplicitRate() As Double
        ' Calculate the implicit interest rate
        Dim monthlyRate As Double
        On Error Resume Next
        monthlyRate = Rate(m_monthsToPayoff, -m_minimumPayment, m_balance)
        If Err.Number = 0 Then
            GetImplicitRate = monthlyRate * 12  ' Annual rate
        Else
            GetImplicitRate = -1
            Err.Clear
        End If
        On Error GoTo 0
    End Function
    Public Function GetTotalInterest() As Double
        GetTotalInterest = (m_minimumPayment * m_monthsToPayoff) - m_balance
    End Function
    Public Function GetInterestAsPercent() As Double
        GetInterestAsPercent = GetTotalInterest() / m_balance
    End Function
    Public Function CompareToFixedPayment(fixedPayment As Double) As String
        Dim result As String
        Dim currentRate As Double
        Dim fixedMonths As Integer
        Dim savings As Double
        currentRate = GetImplicitRate()
        If currentRate < 0 Then
            CompareToFixedPayment = "Error calculating current rate"
            Exit Function
        End If
        ' Calculate months to pay off with fixed payment
        fixedMonths = NPer(currentRate / 12, -fixedPayment, m_balance)
        savings = (m_minimumPayment * m_monthsToPayoff) - (fixedPayment * fixedMonths)
        result = "Current Plan:" & vbCrLf
        result = result & "  Payment: $" & Format(m_minimumPayment, "#,##0.00") & vbCrLf
        result = result & "  Months: " & m_monthsToPayoff & vbCrLf
        result = result & "  Total: $" & Format(m_minimumPayment * m_monthsToPayoff, "#,##0.00") & vbCrLf
        result = result & vbCrLf & "Fixed Payment Plan:" & vbCrLf
        result = result & "  Payment: $" & Format(fixedPayment, "#,##0.00") & vbCrLf
        result = result & "  Months: " & fixedMonths & vbCrLf
        result = result & "  Total: $" & Format(fixedPayment * fixedMonths, "#,##0.00") & vbCrLf
        result = result & vbCrLf & "Savings: $" & Format(savings, "#,##0.00")
        CompareToFixedPayment = result
    End Function
End Class

Error Handling

The Rate function can raise errors in the following situations: - Invalid Procedure Call (Error 5): When: - The function cannot find a solution after 20 iterations - nper is 0 or negative - pmt and pv have the same sign (both positive or both negative) - Type Mismatch (Error 13): When arguments cannot be converted to numeric values - Overflow (Error 6): When calculated values exceed Double range Always use error handling when calling Rate:

On Error Resume Next
interestRate = Rate(nper, pmt, pv, fv, type, guess)
If Err.Number <> 0 Then
    MsgBox "Error calculating rate: " & Err.Description
    interestRate = -1  ' Error indicator
    Err.Clear
End If
On Error GoTo 0

Performance Considerations

• The Rate function uses an iterative algorithm (Newton-Raphson method)
• Each call may require multiple iterations (up to 20) to converge
• Providing a good guess value can significantly speed up convergence
• Poor initial guesses can cause failure to converge or slower performance
• Consider caching results if the same parameters are used repeatedly

Best Practices

1. Validate Inputs: Check that payment and PV have opposite signs
2. Use Error Handling: Always wrap Rate calls in error handlers
3. Provide Good Guesses: Supply reasonable guess values for faster convergence
4. Retry with Different Guesses: If Rate fails, try different guess values
5. Convert to Annual Rate: Multiply monthly rate by 12 for APR
6. Check for Reasonableness: Validate that calculated rate is realistic
7. Include Fees in APR: Calculate effective APR by including all fees
8. Use APY for Compounding: Calculate APY when showing compound returns
9. Document Assumptions: Clearly state what the rate represents
10. Validate Results: Verify Rate result by using it in Pmt or PV calculation

Comparison with Related Functions

Platform and Version Notes

• Available in all versions of VBA and VB6
• Uses iterative algorithm that may not always converge
• Maximum 20 iterations before failure
• Results may vary slightly between platforms due to floating-point precision
• Default guess of 0.1 (10%) works well for most common scenarios

Limitations

• May fail to converge for some parameter combinations
• Limited to 20 iterations maximum
• Cannot handle multiple solutions (returns first solution found)
• Sensitive to initial guess value
• May return unrealistic rates if inputs are invalid
• Cannot handle variable rate scenarios
• Assumes constant periodic payments

Related Functions

• Pmt: Returns the periodic payment for an annuity
• PV: Returns the present value of an annuity
• FV: Returns the future value of an annuity
• NPer: Returns the number of periods for an annuity
• IRR: Returns internal rate of return for irregular cash flows
• MIRR: Returns modified internal rate of return