# Annuity Calculator

Updated on April 17, 2024
Article byWallstreetmojo Team
Edited byWallstreetmojo Team
Reviewed byDheeraj Vaidya, CFA, FRM

## What Is An Annuity Calculator?

An annuity calculator refers to the tool that helps calculate the series of regular payments to be received in the future, either at the end or the beginning of the period. The one to be received at the beginning of the period is called an annuity due, and the one received at the end of the period is known as an ordinary period.

#### Annuity Calculator

r * PVADue / [ {1 – (1+r)-n} * (1+r) ]

Wherein,
• PVADue is the Present Value of an annuity due
• r is the rate of interest per annum
• n is the number of period or frequency wherein annuity will be received
\$
%

It also helps assess the growth in the annuity figure depending on the fluctuations, including the optional additions happening monthly or annually. Besides these additions, there are other elements also that these calculators use to ensure the calculated amounts are accurate and per the market rates. Such components pr factors include annual growth rate, starting principal and annual or monthly additions detail.

### Annuity Calculator Explained

Annuity calculator has been designed to help investors calculate their payments due with the insurance companies depending on different factors. They can calculate how much to pay to generate a specific income at the end of maturity. In the United States, annuities can be retirement plans for salaried people as here they can receive a fixed amount per their requirement, which can be either annual, monthly, or quarterly payments as desired. Big financial institutions such as banks, insurance companies, etc., create most annuities to generate regular fixed income for their clients.

There are two types of annuity: one is received at the beginning of the period, and another is to be received at the end. The only difference between the two is that the first installment will also be used to calculate interest for an annuity to be received at the end of the period. In another one, since it’s at the start of the period, there would be one period less for calculating interest. The reason could be that interest not received for 1st annuity calculator payment could be invested in the market and earn interest. This equation is helpful for the person to calculate what annuity amount will be received at regular intervals and, accordingly, one can invest. This tool can also calculate the amortization of loans, structured settlements, income annuities, or lottery payouts.

### Formula

The formula on which the retirement annuity calculator mostly works is mentioned below:

1) Annuity Due

Mathematically it can be calculated:

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

2) Ordinary Annuity

Mathematically it can be calculated:

r * PVA Ordinary / [ 1 – (1+r)-n ]

Wherein,

• PVA Due is the Present Value of an annuity due
• PVA Ordinary is the Present Value of an ordinary annuity
• r is the rate of interest per annum
• n is the number of periods or frequency wherein annuity will be received

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### How To Calculate Using Annuity Calculator?

One needs to follow the below steps to calculate the annuity amounts.

• First, determine the amount to be invested in an annuity and whether it is an ordinary annuity or annuity due.
• The second step would be to calculate the interest rate, which is applicable and should be determined rate per period by dividing the rate by the number of periodic payments in the year.
• Now, determine the number of periods by multiplying the period for which annuity is taken with the number of periodic payments in a year, which is ‘n’ of the equation.
• Finally, determine the annuity value based on its type, as discussed above.
• The resultant figure would be annuity per period.

### Examples

Let us consider the following instances to understand how the calculator can be used to find out accurate figures:

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

#### Example #1

Mr. Punk was trying his luck and had spent too much on buying the lottery tickets. He buys the lottery ticket for the last time for \$1,000, where the winning price is \$1,000,000, and the number of participants is less. This time his luck shines, and he won the lottery with a 20% tax deduction of 20%. He decides to invest in an annuity that shall pay him in yearly installments at the end of each year for the next 25 years. The ongoing market rate of interest is 5.67%.

Based on the given information, you must calculate the installment amount Mr. Punk would receive at the end of each year.

Solution

This question pertains to an ordinary annuity that pays a fixed amount at the end of the year. The amount that would be invested is \$1,000,000, less than 20% tax, which is \$800,000. We can now use the below formula to calculate the annuity amount. n would be 25 years since it’s paid annually, and the interest rate is 5.67% per annum.

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

Enter =5.67% x 800,000 / [1 – (1 + 5.67%)-25 ]

• You will get a value as 60,632.62

Therefore, Mr. Punk would be eligible to be received a fixed amount of \$60,632.62 for the next 25 years.

#### Example #2

He is continuing the same example above, assuming that Mr. Punk desires to receive the fixed amounts at the start of the year since he would be in the immediate requirement, and the company agrees. Now the annuity that will be received shall be paid at the beginning of the year, and you are required to calculate the new fixed annuity amount to be received by Mr. Punk in this case.

Solution

This question now pertains to annuity due, which pays a fixed amount at the beginning of the year. The amount that would be invested is \$1,000,000, less than 20% tax, which is \$800,000. Then we can now use the below formula to calculate the annuity amount. n would be 25 years since it’s paid annually, and the interest rate is 5.67% per annum.

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

Enter =5.67% x 800,000 / [1 – (1 + 5.67%)-25 * (1 + 5.67%)]

• You will get a value as 57,379.22

Therefore, Mr. Punk would be eligible to receive a fixed amount of \$57,379.22 for the next 25 years.

Hence it can be concluded that in the case of the annuity, the amount would be less than the amount to be received in the case of an ordinary annuity.

### Uses

With the help of the annuity calculator, an individual has a tool that they can use to calculate the following:

• The amount that one needs to invest or pay to get back a specific amount at maturity. This means, one can invest an amount that would help them generate the sufficient income they would require when they get old.
• The amount to be paid that would deplete the fund over a period.
• The number of years for which this investment would help generate payments at the specific rate.

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