Annuity Calculator

Annuity calculator can be used to calculate the series of regular payments which are to be received in future either at the end of the period or at the beginning of the period and the one which is to be received at the beginning of the period is called an annuity due and the one which is received at the end of the period is known as ordinary period.

Annuity Calculator

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

Wherein,

PVA_Due 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

PVA_Due

About Annuity Calculator

There are two types of annuity one which is received at the beginning of the period and another one which is to be received at the end of the period. 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 end of the period and in another one since it’s at the start of the period there would be one period less for calculation of interest. The reason could be for interest not received for 1^st payment could be invested in the market and can earn interest. This equation is helpful for the person to calculate what annuity amount will be received at regular intervals and accordingly one can make an investment. This calculator can also be used to calculate the amortization of loans, structured settlements, income annuities or lottery pay-outs.

The formula for calculating Annuity as per 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 _Ordinaryis the Present Value of an ordinary annuity
r is the rate of interest per annum
n is the number of period or frequency wherein annuity will be received

How to Calculate using the Annuity Calculator?

One needs to follow the below steps in order to calculate the annuity amounts.
First of all, determine the amount that is to be invested in 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 the 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 upon its type which is as discussed above.
The resultant figure would be annuity per period.

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

Example #1

Mr. Punk was trying his luck and has spent too much on buying the lottery tickets. He decides to buy 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 amount less 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 are required to calculate what shall be the installment amount that 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 rate of interest 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 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

Continuing the same example above, assuming now that the Mr. Punk desires to receive the fixed amounts at the start of the year since he would be in immediate requirement and the company agrees to same and now the annuity that will be received shall be paid at the beginning of the year, 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 rate of interest 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 value as 57,379.22

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

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

Conclusion

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 that may be desired. Most of the annuities are created by big financial institutions such as banks, insurance companies, etc. so as to generate regular fixed income for their clients.
Further, there are even other types of annuities other than fixed annuity such as a variable annuity, perpetuity annuities, life annuities, etc. Further by deferring payments, one could also receive tax benefits on the same depending upon the tax jurisdiction the person belongs to. However, one also needs to be aware of the charges that are applied in annuities.