Financial Modeling Tutorials
 Financial Modeling Basics
 Excel Modeling
 Financial Functions in Excel
 Sensitivity Analysis in Excel
 Time Value of Money
 Future Value Formula
 Present Value Factor
 Perpetuity Formula
 Present Value vs Future Value
 Annuity vs Pension
 Present Value of an Annuity
 Doubling Time Formula
 Annuity Formula
 Annuity vs Perpetuity
 Annuity vs Lump Sum
 Internal Rate of Return (IRR)
 NPV vs XNPV
 NPV vs IRR
 NPV Formula
 PV vs NPV
 IRR vs ROI
 Break Even Point
 Payback Period & Discounted Payback Period
 Payback period Formula
 Discounted Payback Period Formula
 Profitability Index
 Cash Burn Rate
 Simple Interest
 Simple Interest vs Compound Interest
 Simple Interest Formula
 CAGR Formula (Compounded Annual Growth Rate)
 Effective Interest Rate
 Loan Amortization Schedule
 Mortgage Formula
 Loan Principal Amount
 Interest Rate Formula
 Rate of Return Formula
 Effective Annual Rate
 Effective Annual Rate Formula (EAR)
 Daily Compound Interest
 Monthly Compound Interest Formula
 Discount Rate vs Interest Rate
 Rule of 72
 Geometric Mean Return
 Real Rate of Return Formula
 Continuous compounding Formula
 Weighted average Formula
 Average Formula
 Average Rate of Return Formula
 Mean Formula
 Weighted Mean Formula
 Harmonic Mean Formula
 Median Formula in Statistics
 Range Formula
 Expected Value Formula
 Exponential Growth Formula
 Margin of Error Formula
 Decrease Percentage Formula
 Percent Error Formula
 Holding Period Return Formula
 Cost Benefit Analysis
 Cost Volume Profit Analysis
 Opportunity Cost Formula
 Mortgage APR vs Interest Rate
 Regression Formula
 Correlation Coefficient Formula
 Covariance Formula
 Coefficient of Variation Formula
 Sample Standard Deviation Formula
 Relative Standard Deviation Formula
 Volatility Formula
 Binomial Distribution Formula
 Quartile Formula
 P Value Formula
 Skewness Formula
 Regression vs ANOVA
What is the Annuity Formula?
The term “annuity” refers to the series of periodic payments to be received either at the beginning of each period or at the end of the period in the future. If the payment is received at the end of each period then it is called ordinary annuity while in the other case it is called annuity due.
The equation for annuity payment based on PV of an ordinary annuity is calculated based on PV of an ordinary annuity, effective interest rate and a number of periods.
Mathematically, the equation for an ordinary annuity is represented as,
where,
 PVA _{Ordinary} = Present value of an ordinary annuity
 r = Effective interest rate
 n = Number of periods
The equation for annuity payment an annuity due is calculated based on PV of an annuity due, effective interest rate and a number of periods.
Mathematically, the equation for annuity due is represented as,
where,
 PVA _{Due} = Present value of an annuity due
 r = Effective interest rate
 n = Number of periods
Explanation of the Annuity Formula
The formula for the calculation of annuity payment can be derived by using the PV of ordinary annuity in the following steps:
Step 1: Firstly, determine the PV of the annuity and confirm that the payment will be done at the end of each period. It is denoted by PVA _{Ordinary}.
Step 2: Next, determine the interest rate on the basis of the current market return. Then, the effective rate of interest is computed by dividing the annualized interest rate by the number of periodic payments in a year and it is denoted by r.
r = Annualized interest rate / Number periodic payments in a year
Step 3: Next, determine the number of periods by multiplying the number of periodic payments in a year and the number of years and it is denoted by n.
n = Number of periodic payments in a year * Number of years
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Step 4: Finally, the formula for annuity payment based on PV of an ordinary annuity is calculated based on PV of ordinary annuity (step 1), effective interest rate (step 2) and a number of periods (step 3) as shown above.
The formula for the calculation of annuity payment can also be derived by using the PV of an annuity due in the following steps:
Step 1: Firstly, determine the PV of the annuity and confirm that the payment will be done at the beginning of each period. It is denoted by PVA _{Due}.
Step 2: Next, determine the interest rate on the basis of the current market return. Then, the effective rate of interest is computed by dividing the annualized interest rate by the number of periodic payments in a year and it is denoted by r.
r = Annualized interest rate / Number periodic payments in a year
Step 3: Next, determine the number of periods by multiplying the number of periodic payments in a year and the number of years and it is denoted by n.
n = Number of periodic payments in a year * Number of years
Step 4: Finally, the equation for annuity payment based on PV of an annuity due is calculated based on PV of annuity due (step 1), effective interest rate (step 2) and a number of periods (step 3) as shown above.
Examples of Annuity Formula (with Excel Template)
Let’s see some simple to advanced examples of annuity formula to understand it better.
Example #1
Let us take the example of David who won a lottery worth $10,000,000. He has opted for an annuity payment at the end of each year for the next 20 years as a payout option. Determine the amount that David will be paid as annuity payment if the ongoing rate of interest in the market is 5%.
Given below is the data used for the calculation of annuity payments.
PVA _{Ordinary} = $10,000,000 (since the annuity to be paid at the end of each year)
Therefore, the calculation of annuity payment can be done using the above formula as,
 Annuity = 5% * $10,000,000 / [1 – (1 + 5%)^{20}]
Calculation of Annuity Payment will be –
 Annuity = $802,425.87 ~ $802,426
Therefore, David will pay annuity payments of $802,426 for the next 20 years in case of ordinary annuity.
Example #2
Let us take the above example of David and determine the annuity payment if it is paid at the beginning of each year with all other conditions the same.
We will use the same data as the above example for the calculation of Annuity payments.
Therefore, the calculation of annuity payment can be done using the above formula as,
 Annuity = r * PVA _{Due} / [{1 – (1 + r)^{n}} * (1 + r)]
 Annuity = 5% * $10,000,000 / [{1 – (1 + 5%)^{20}} * (1 + 5%)]
Calculation of Annuity Payment will be –
 Annuity = $764,215.12 ~ $764,215
Therefore, David will pay annuity payments of $764,215 for the next 20 years in case of annuity due.
Annuity Formula
You can use the following Annuity Formula Calculator.
PVA Ordinary  
r  
n  
Annuity Formula =  
Annuity Formula =  r * 
 
0 * 

Relevance and Uses
The annuity payment is one of the applications of the time value of money which is further indicated by the difference between annuity payments based on ordinary annuity and annuity due. The reason for lower annuity payment for an annuity due is that the money is received at the start of each period and as such, it is believed that the money will be invested in the market and interest will be earned during that period.
The equation for annuity payment finds application in the calculation of income annuities, amortized loans, lottery payouts, structured settlements and any other type of fixed periodic payments.
Recommended Articles
This has been a guide to Annuity Formula. Here we discuss how to calculate Annuity Payments in Excel for Ordinary and due annuity using its formula along with practical examples and downloadable excel template. You can learn more about financial analysis from the following articles –
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