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