WallStreetMojo

WallStreetMojo

WallStreetMojo

MENUMENU
  • Blog
  • Free Video Tutorials
  • Courses
  • All In One Bundle
  • Login
Home » Financial Modeling Tutorials » Excel Modeling » Annuity Formula

Annuity Formula

By Madhuri ThakurMadhuri Thakur | Reviewed By Dheeraj VaidyaDheeraj Vaidya, CFA, FRM

Formula to Calculate Annuity Payment

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. The formula for annuity payment and annuity due is calculated based on PV of an annuity due, effective interest rate and a number of periods.

The formula based on an ordinary annuity is calculated based on PV of an ordinary annuity, effective interest rate, and several periods.

Annuity = r * PVA Ordinary / [1 – (1 + r)-n]

where,

  • PVA Ordinary = Present value of an ordinary annuity
  • r = Effective interest rate
  • n = Number of periods

 

Mathematically, the equation for annuity due is represented as,

Annuity = r * PVA Due / [{1 – (1 + r)-n} * (1 + r)]

where,

  • PVA Due = Present value of an annuity due
  • r = Effective interest rate
  • n = number of periods

ANNUITY-FORMULA

How to Calculate Annuity Payment? (Step by Step)

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 made at the end of each period. It is denoted by PVA Ordinary.
  • Step 2: Next, determine the interest rate based on 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 regular 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 regular payments in a year * Number of years
  • Step 4: Finally, the annuity payment based on PV of an ordinary annuity is calculated based on PV of an ordinary annuity (step 1), effective interest rate (step 2), and some periods (step 3), as shown above.

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 made at the beginning of each period. It is denoted by PVA Due.
  • Step 2: Next, determine the interest rate based on 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 regular 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 regular payments in a year * Number of years
  • Step 4: Finally, the annuity payment based on PV of an annuity due is calculated based on PV of an annuity due (step 1), effective interest rate (step 2), and several periods (step 3), as shown above.

Examples

You can download this Annuity Formula Excel Template here – Annuity Formula Excel Template

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 constant rate of interest in the market is 5%.

Given below is the data used for the calculation of annuity payments.

Popular Course in this category
Sale
All in One Financial Analyst Bundle (250+ Courses, 40+ Projects)
4.9 (1,067 ratings)
250+ Courses | 40+ Projects | 1000+ Hours | Full Lifetime Access | Certificate of Completion
View Course

annuity formula example 1.1

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 as follows –

annuity formula example 1.2

  • Annuity = 5% * $10,000,000 / [1 – (1 + 5%)-20]

Calculation of Annuity Payment will be –

annuity formula example 1.3

  • 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 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.

example 2.1

Therefore, the calculation of annuity payment can be done as follows –

example 2.2

  • 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 –

example 2.3

  • Annuity = $764,215.12 ~ $764,215

Therefore, David will pay annuity payments of $764,215 for the next 20 years in case of an annuity due.

Annuity Calculator

You can use the following Annuity Calculator.

PVA Ordinary
r
n
Annuity Formula =
 

Annuity Formula = r *
PVA Ordinary
[1 -(1 + r)-n]
0 *
0
= 0
[1 -(1 + 0)−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 lower annuity payment for an annuity is that the money is received at the start of each period. It is believed that the funds will be invested in the market, and interest will be earned during that period.

The equation for annuity payment finds application in calculating income annuities, amortized loans, lottery pay-outs, structured settlements, and any other type of fixed periodic payments.

Annuity Formula Video

Recommended Articles

This article has been a guide to Annuity Formula. Here we learn how to calculate Annuity Payments for Ordinary and due annuity along with practical examples and a downloadable excel template. You can know more about financial analysis from the following articles –

  • Annuity vs. Perpetuity
  • Effective Annual Rate Formula
  • Formula of Present Value of an Annuity 
  • Tax-Deferred Annuity
10 Shares
Share
Tweet
Share
All in One Financial Analyst Bundle (250+ Courses, 40+ Projects)
  • 250+ Courses
  • 40+ Projects
  • 1000+ Hours
  • Full Lifetime Access
  • Certificate of Completion
LEARN MORE >>
Primary Sidebar
Footer
COMPANY
About
Reviews
Contact
Privacy
Terms of Service
RESOURCES
Blog
Free Courses
Free Tutorials
Investment Banking Tutorials
Financial Modeling Tutorials
Excel Tutorials
Accounting Tutorials
Financial Statement Analysis
COURSES
All Courses
Financial Analyst All in One Course
Investment Banking Course
Financial Modeling Course
Private Equity Course
Venture Capital Course
Excel All in One Course

Copyright © 2021. CFA Institute Does Not Endorse, Promote, Or Warrant The Accuracy Or Quality Of WallStreetMojo. CFA® And Chartered Financial Analyst® Are Registered Trademarks Owned By CFA Institute.
Return to top

WallStreetMojo

Download Coursera IPO Financial Model

By continuing above step, you agree to our Terms of Use and Privacy Policy.
WallStreetMojo

Free Investment Banking Course

IB Excel Templates, Accounting, Valuation, Financial Modeling, Video Tutorials

* Please provide your correct email id. Login details for this Free course will be emailed to you

Book Your One Instructor : One Learner Free Class
WallStreetMojo

Free Investment Banking Course

IB Excel Templates, Accounting, Valuation, Financial Modeling, Video Tutorials

* Please provide your correct email id. Login details for this Free course will be emailed to you

Let’s Get Started
Please select the batch
Saturday - Sunday 9 am IST to 5 pm IST
Saturday - Sunday 9 am IST to 5 pm IST

This website or its third-party tools use cookies, which are necessary to its functioning and required to achieve the purposes illustrated in the cookie policy. By closing this banner, scrolling this page, clicking a link or continuing to browse otherwise, you agree to our Privacy Policy

Login

Forgot Password?

WallStreetMojo

Download Annuity Formula Excel Template

Coursera IPO Financial Model & Valuation Free Download