Fv Function

Returns a Double specifying the future value of an annuity based on periodic, fixed payments and a fixed interest rate.

Syntax

Fv(rate, nper, pmt[, pv[, type]])

Parameters

• rate - Required. Double specifying interest rate per period. For example, if you get a car loan at an annual percentage rate (APR) of 10 percent and make monthly payments, the rate per period is 0.1/12, or 0.0083.
• nper - Required. Integer specifying total number of payment periods in the annuity. For example, if you make monthly payments on a four-year car loan, your loan has a total of 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 - Optional. Variant specifying present value (or lump sum) of a series of future payments. 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. 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.

Return Value

Returns a Double representing the future value of an annuity based on periodic, fixed payments and a fixed interest rate.

Remarks

• 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).
• The rate and nper arguments must be calculated using payment periods expressed in the same units.
• For example, if rate is calculated using months, nper must also be calculated using months.
• 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.
• Fv is related to the Pv function. Fv calculates what a series of payments will be worth in the future, while Pv calculates what a series of future payments is worth now.

Typical Uses

• Calculating savings account balance after regular deposits
• Determining investment portfolio value after periodic contributions
• Computing retirement fund balance
• Estimating college savings fund growth
• Analyzing long-term investment returns
• Planning for future financial goals

Basic Usage Examples

' Calculate future value of monthly savings
Dim monthlyDeposit As Double
Dim annualRate As Double
Dim years As Integer
Dim futureValue As Double

monthlyDeposit = -100  ' $100 per month (negative because it's paid out)
annualRate = 0.06      ' 6% annual interest
years = 10

' Calculate future value
futureValue = Fv(annualRate / 12, years * 12, monthlyDeposit)
' Returns approximately $16,387.93

' Calculate future value with initial deposit
Dim initialDeposit As Double
initialDeposit = -1000  ' $1000 initial deposit

futureValue = Fv(annualRate / 12, years * 12, monthlyDeposit, initialDeposit)
' Returns approximately $18,193.97

' Calculate with payments at beginning of period
futureValue = Fv(annualRate / 12, years * 12, monthlyDeposit, initialDeposit, 1)
' Returns approximately $18,284.68

' Calculate investment growth with no regular payments
Dim lumpSum As Double
lumpSum = -5000  ' $5000 one-time investment

futureValue = Fv(0.08 / 12, 5 * 12, 0, lumpSum)
' Returns approximately $7,449.23 (compound interest on lump sum)

Common Patterns

1. Monthly Savings Calculator

Function CalculateSavings(monthlyAmount As Double, years As Integer, _
annualRate As Double) As Double
Dim monthlyRate As Double
Dim periods As Integer

monthlyRate = annualRate / 12
periods = years * 12

' Negative because it's money paid out
CalculateSavings = Fv(monthlyRate, periods, -monthlyAmount)
End Function

' Usage
Dim savings As Double
savings = CalculateSavings(200, 20, 0.07)  ' $200/month, 20 years, 7%
MsgBox "Future value: " & FormatCurrency(savings)

2. Retirement Planning

Function CalculateRetirementFund(monthlyContribution As Double, _
currentAge As Integer, _
retirementAge As Integer, _
currentBalance As Double, _
expectedReturn As Double) As Double
Dim years As Integer
Dim periods As Integer
Dim monthlyRate As Double

years = retirementAge - currentAge
periods = years * 12
monthlyRate = expectedReturn / 12

CalculateRetirementFund = Fv(monthlyRate, periods, _
-monthlyContribution, _
-currentBalance)
End Function

' Usage
Dim retirementValue As Double
retirementValue = CalculateRetirementFund(500, 30, 65, 10000, 0.08)
Debug.Print "Retirement fund at 65: " & FormatCurrency(retirementValue)

3. College Savings Plan

Function CollegeSavingsPlan(yearsUntilCollege As Integer, _
monthlyDeposit As Double, _
initialAmount As Double, _
expectedRate As Double) As Double
Dim monthlyRate As Double
Dim periods As Integer

monthlyRate = expectedRate / 12
periods = yearsUntilCollege * 12

CollegeSavingsPlan = Fv(monthlyRate, periods, _
-monthlyDeposit, _
-initialAmount)
End Function

' Usage
Dim collegeFund As Double
collegeFund = CollegeSavingsPlan(18, 250, 5000, 0.06)
MsgBox "College fund in 18 years: " & FormatCurrency(collegeFund)

4. Investment Comparison

Sub CompareInvestments()
Dim option1 As Double
Dim option2 As Double
Dim years As Integer

years = 10

' Option 1: $100/month at 6%
option1 = Fv(0.06 / 12, years * 12, -100)

' Option 2: $50/month at 8%
option2 = Fv(0.08 / 12, years * 12, -50)

Debug.Print "Option 1 (6%): " & FormatCurrency(option1)
Debug.Print "Option 2 (8%): " & FormatCurrency(option2)

If option1 > option2 Then
Debug.Print "Option 1 is better"
Else
Debug.Print "Option 2 is better"
End If
End Sub

5. Compound Interest Calculator

Function CompoundInterest(principal As Double, rate As Double, _
years As Integer, _
Optional compoundFrequency As Integer = 12) As Double
Dim periods As Integer
Dim periodRate As Double

periods = years * compoundFrequency
periodRate = rate / compoundFrequency

' No periodic payment, just compound the principal
CompoundInterest = Fv(periodRate, periods, 0, -principal)
End Function

' Usage
Dim finalAmount As Double
finalAmount = CompoundInterest(10000, 0.05, 10, 12)  ' Monthly compounding
Debug.Print "Principal grows to: " & FormatCurrency(finalAmount)

6. Savings Goal Calculator

Function MonthlyDepositNeeded(targetAmount As Double, _
years As Integer, _
rate As Double, _
Optional startingBalance As Double = 0) As Double
' This is the inverse - given FV, find PMT
' Using trial and error or formula
Dim monthlyRate As Double
Dim periods As Integer

monthlyRate = rate / 12
periods = years * 12

' Use Pmt function instead for accurate calculation
' This example shows how Fv relates to the goal
Dim testPayment As Double
testPayment = 100

Do While Fv(monthlyRate, periods, -testPayment, -startingBalance) < targetAmount
testPayment = testPayment + 10
Loop

MonthlyDepositNeeded = testPayment
End Function

7. Annuity Future Value

Function AnnuityFutureValue(payment As Double, rate As Double, _
years As Integer, _
paymentTiming As Integer) As Double
' paymentTiming: 0 = end of period, 1 = beginning of period
Dim periods As Integer

periods = years
AnnuityFutureValue = Fv(rate, periods, -payment, 0, paymentTiming)
End Function

' Usage
Dim fvOrdinary As Double
Dim fvDue As Double

fvOrdinary = AnnuityFutureValue(1000, 0.05, 10, 0)  ' Ordinary annuity
fvDue = AnnuityFutureValue(1000, 0.05, 10, 1)       ' Annuity due

Debug.Print "Ordinary annuity FV: " & FormatCurrency(fvOrdinary)
Debug.Print "Annuity due FV: " & FormatCurrency(fvDue)

8. Investment Portfolio Projection

Type PortfolioProjection
Years As Integer
FutureValue As Double
End Type

Function ProjectPortfolio(monthlyDeposit As Double, _
startingBalance As Double, _
rate As Double, _
maxYears As Integer) As PortfolioProjection()
Dim projections() As PortfolioProjection
Dim i As Integer
Dim monthlyRate As Double

ReDim projections(1 To maxYears)
monthlyRate = rate / 12

For i = 1 To maxYears
projections(i).Years = i
projections(i).FutureValue = Fv(monthlyRate, i * 12, _
-monthlyDeposit, _
-startingBalance)
Next i

ProjectPortfolio = projections
End Function

9. Loan Payoff Calculator (Inverse Use)

Sub AnalyzeLoanPayoff()
Dim loanAmount As Double
Dim monthlyPayment As Double
Dim annualRate As Double
Dim years As Integer
Dim remainingBalance As Double

loanAmount = 200000     ' Initial loan
monthlyPayment = 1200   ' Monthly payment
annualRate = 0.045      ' 4.5% APR
years = 5               ' After 5 years

' Future value will be negative (debt remaining)
remainingBalance = -Fv(annualRate / 12, years * 12, _
monthlyPayment, -loanAmount)

Debug.Print "Remaining balance after " & years & " years: " & _
FormatCurrency(remainingBalance)
End Sub

10. Recurring Deposit Calculator

Sub RecurringDepositCalculator()
Dim deposit As Double
Dim rate As Double
Dim quarters As Integer
Dim maturityValue As Double

deposit = 500           ' Quarterly deposit
rate = 0.06 / 4        ' Quarterly rate (6% annual)
quarters = 20          ' 5 years

maturityValue = Fv(rate, quarters, -deposit)

Debug.Print "Maturity value: " & FormatCurrency(maturityValue)
Debug.Print "Total deposits: " & FormatCurrency(deposit * quarters)
Debug.Print "Interest earned: " & _
FormatCurrency(maturityValue - (deposit * quarters))
End Sub

Advanced Usage

1. Flexible Savings Calculator with UI

Sub CalculateAndDisplay()
Dim monthlyDeposit As Double
Dim years As Integer
Dim annualRate As Double
Dim initialBalance As Double
Dim paymentType As Integer
Dim futureValue As Double

' Get inputs from form controls
monthlyDeposit = CDbl(txtMonthlyDeposit.Text)
years = CInt(txtYears.Text)
annualRate = CDbl(txtRate.Text) / 100
initialBalance = CDbl(txtInitialBalance.Text)

' Check if payments at beginning or end
paymentType = IIf(chkBeginning.Value = 1, 1, 0)

' Calculate
futureValue = Fv(annualRate / 12, years * 12, _
-monthlyDeposit, _
-initialBalance, _
paymentType)

' Display result
lblResult.Caption = "Future Value: " & FormatCurrency(futureValue, 2)

' Calculate total contributions
Dim totalContributions As Double
totalContributions = initialBalance + (monthlyDeposit * years * 12)

' Calculate interest earned
Dim interestEarned As Double
interestEarned = futureValue - totalContributions

lblTotalDeposits.Caption = "Total Deposits: " & _
FormatCurrency(totalContributions, 2)
lblInterest.Caption = "Interest Earned: " & _
FormatCurrency(interestEarned, 2)
End Sub

2. Scenario Analysis

Sub AnalyzeScenarios()
Dim rates() As Double
Dim deposit As Double
Dim years As Integer
Dim i As Integer

deposit = 300
years = 15
rates = Array(0.04, 0.06, 0.08, 0.10)  ' Different return scenarios

Debug.Print "Scenario Analysis for $" & deposit & "/month over " & years & " years:"
Debug.Print String(60, "=")

For i = LBound(rates) To UBound(rates)
Dim fv As Double
fv = Fv(rates(i) / 12, years * 12, -deposit)

Debug.Print "At " & FormatPercent(rates(i), 0) & ": " & _
FormatCurrency(fv, 2) & " (gain: " & _
FormatCurrency(fv - (deposit * years * 12), 2) & ")"
Next i
End Sub

3. Goal-Based Planning

Function YearsToReachGoal(targetAmount As Double, _
monthlyDeposit As Double, _
startingBalance As Double, _
annualRate As Double) As Double
Dim years As Double
Dim fv As Double
Dim monthlyRate As Double

monthlyRate = annualRate / 12
years = 1

Do While years <= 50  ' Max 50 years
fv = Fv(monthlyRate, years * 12, -monthlyDeposit, -startingBalance)

If fv >= targetAmount Then
YearsToReachGoal = years
Exit Function
End If

years = years + 0.25  ' Check quarterly
Loop

YearsToReachGoal = -1  ' Goal not reachable
End Function

' Usage
Dim yearsNeeded As Double
yearsNeeded = YearsToReachGoal(500000, 1000, 50000, 0.07)

If yearsNeeded > 0 Then
MsgBox "You will reach your goal in " & Format(yearsNeeded, "0.0") & " years"
Else
MsgBox "Goal not reachable with current parameters"
End If

4. Monte Carlo Simulation

Function SimulateFutureValue(deposit As Double, years As Integer, _
avgRate As Double, volatility As Double, _
simulations As Integer) As Variant
Dim results() As Double
Dim i As Integer
Dim simulatedRate As Double

ReDim results(1 To simulations)
Randomize

For i = 1 To simulations
' Simple random variation around average rate
simulatedRate = avgRate + ((Rnd() - 0.5) * 2 * volatility)

' Ensure rate doesn't go negative
If simulatedRate < 0 Then simulatedRate = 0

results(i) = Fv(simulatedRate / 12, years * 12, -deposit)
Next i

SimulateFutureValue = results
End Function

' Analyze results
Sub AnalyzeSimulation()
Dim results As Variant
Dim avg As Double, minVal As Double, maxVal As Double
Dim i As Integer

results = SimulateFutureValue(500, 20, 0.07, 0.02, 1000)

avg = 0
minVal = 1E+308
maxVal = -1E+308

For i = 1 To UBound(results)
avg = avg + results(i)
If results(i) < minVal Then minVal = results(i)
If results(i) > maxVal Then maxVal = results(i)
Next i

avg = avg / UBound(results)

Debug.Print "Average FV: " & FormatCurrency(avg, 2)
Debug.Print "Min FV: " & FormatCurrency(minVal, 2)
Debug.Print "Max FV: " & FormatCurrency(maxVal, 2)
End Sub

5. Tax-Advantaged Account Calculator

Function TaxAdvantaged401k(salary As Double, contributionPct As Double, _
employerMatch As Double, years As Integer, _
currentBalance As Double, rate As Double) As Double
Dim monthlyContribution As Double
Dim monthlyEmployerMatch As Double
Dim totalMonthlyDeposit As Double

' Calculate monthly contributions
monthlyContribution = (salary * contributionPct) / 12
monthlyEmployerMatch = (salary * employerMatch) / 12
totalMonthlyDeposit = monthlyContribution + monthlyEmployerMatch

TaxAdvantaged401k = Fv(rate / 12, years * 12, _
-totalMonthlyDeposit, _
-currentBalance)
End Function

' Usage
Dim retirement401k As Double
retirement401k = TaxAdvantaged401k(75000, 0.06, 0.03, 30, 25000, 0.08)
Debug.Print "401(k) at retirement: " & FormatCurrency(retirement401k, 2)

6. Education Savings with Increasing Contributions

Function EducationSavingsWithIncrease(initialMonthly As Double, _
annualIncrease As Double, _
years As Integer, _
rate As Double) As Double
Dim yearlyFV As Double
Dim currentMonthly As Double
Dim i As Integer

yearlyFV = 0
currentMonthly = initialMonthly

For i = 1 To years
' Calculate FV for this year's contributions
Dim yearContribution As Double
yearContribution = Fv(rate / 12, (years - i + 1) * 12, _
-currentMonthly)

yearlyFV = yearlyFV + yearContribution

' Increase for next year
currentMonthly = currentMonthly * (1 + annualIncrease)
Next i

EducationSavingsWithIncrease = yearlyFV
End Function

Error Handling

Function SafeFv(rate As Double, nper As Integer, pmt As Double, _
Optional pv As Variant, Optional pType As Variant) As Variant
On Error GoTo ErrorHandler

' Validate inputs
If nper <= 0 Then
SafeFv = "Error: Number of periods must be positive"
Exit Function
End If

If rate <= -1 Then
SafeFv = "Error: Rate must be greater than -100%"
Exit Function
End If

' Set defaults
If IsMissing(pv) Then pv = 0
If IsMissing(pType) Then pType = 0

' Calculate
SafeFv = Fv(rate, nper, pmt, pv, pType)
Exit Function

ErrorHandler:
Select Case Err.Number
Case 5  ' Invalid procedure call
SafeFv = "Error: Invalid arguments"
Case 6  ' Overflow
SafeFv = "Error: Result too large"
Case 13  ' Type mismatch
SafeFv = "Error: Invalid data types"
Case Else
SafeFv = "Error: " & Err.Description
End Select
End Function

Common errors: - Error 5 (Invalid procedure call): Invalid argument values (e.g., negative periods). - Error 6 (Overflow): Result is too large to fit in a Double. - Error 13 (Type mismatch): Arguments are not numeric.

Performance Considerations

• Fv is a mathematical calculation, very fast
• No I/O or external dependencies
• Safe to call repeatedly in loops for scenario analysis
• Consider caching results if using same parameters multiple times
• For large-scale simulations, consider batch calculations

Best Practices

1. Use negative values for cash outflows (payments, deposits)
2. Use positive values for cash inflows (receipts, withdrawals)
3. Match time units - if rate is monthly, nper should be in months
4. Validate inputs - check for reasonable ranges
5. Handle edge cases - zero rate, very long periods
6. Document assumptions - especially for rate projections
7. Consider inflation - future value in today's dollars may differ

Comparison with Other Functions

Fv vs Pv

' Fv: Future value of an investment
futureValue = Fv(0.06 / 12, 10 * 12, -100)  ' What will I have?

' Pv: Present value of an investment
presentValue = Pv(0.06 / 12, 10 * 12, -100)  ' What is it worth today?

Fv vs NPer

' Fv: Calculate future value given payments
fv = Fv(0.05 / 12, 120, -100)

' NPer: Calculate periods needed to reach a goal
periods = NPer(0.05 / 12, -100, 0, 16000)  ' How long to reach $16,000?

Fv vs Pmt

' Fv: Calculate future value given payment amount
fv = Fv(0.06 / 12, 120, -200)

' Pmt: Calculate payment needed to reach future value
payment = Pmt(0.06 / 12, 120, 0, -30000)  ' How much to save for $30,000?

Limitations

• Assumes constant interest rate (real-world rates vary)
• Assumes regular, fixed payments (life is rarely this predictable)
• Does not account for taxes, fees, or inflation
• Does not consider compounding frequency variations
• Limited to Double precision (very large values may overflow)
• No built-in risk or uncertainty modeling

Mathematical Formula

The future value calculation uses the formula:

For type = 0 (payments at end of period):
FV = -PV * (1 + rate)^nper - PMT * [((1 + rate)^nper - 1) / rate]

For type = 1 (payments at beginning of period):
FV = -PV * (1 + rate)^nper - PMT * [((1 + rate)^nper - 1) / rate] * (1 + rate)

Special case when rate = 0:
FV = -PV - PMT * nper

Related Functions

• Pv - Returns the present value of an annuity
• Pmt - Returns the payment for an annuity
• PPmt - Returns the principal payment for a specific period
• IPmt - Returns the interest payment for a specific period
• NPer - Returns the number of periods for an annuity
• Rate - Returns the interest rate per period
• DDB - Returns depreciation using double-declining balance
• SLN - Returns straight-line depreciation
• SYD - Returns sum-of-years' digits depreciation