Present Value Of An Annuity Definition Interpretation

Present Value of an Annuity Definition

Formula

Here,

p1, p2 – Annuity payments,r – Discount raten – Time Period in years

After simplifying this Present value of annuity formula, we can get

p – Equated annual paymentsr – Discount raten – a time period in years

You are free to use this image on you website, templates, etc., Please provide us with an attribution linkHow to Provide Attribution?Article Link to be HyperlinkedFor eg:Source: Present Value of an Annuity (wallstreetmojo.com)

Example #1

Mr. ABC is a 60 years old, retired Government servant. He has been paying into his retirement account per month for the last 30 years, and now, after his retirement, he can start withdrawing funds from the retirement account. As per the agreement, the retirement company is giving him to pay $ 30,000 on the 1st of each year for the next 25 years, or another option is a one-time payment of $ 500,000. Now Mr. ABC wants to know what is the value of the $30,000 yearly payments made to him compared to a one-time payment. He has the option to choose, and he wants to choose, which gives him more money.

Using the present value formula above, we can see that the annuity payments are worth about $400,000 today, assuming an average interest rate of 6 percent. Thus, Mr. Johnson is better off taking the lump sum amount today and investing in himself.

Here, if we change the discount rate, then the present value changes drastically. The discount factorDiscount FactorDiscount Factor is a weighing factor most often used to find the present value of future cash flows, i.e., to calculate the Net Present Value (NPV). It is determined by, 1 / {1 * (1 + Discount Rate) Period Number}read more can be taken based on the interest rates or cost of funds for the company. It depends upon the usage of the discount factor. Thus, the lower the discount rate, the higher the present value.

Example #2

Find out the annuity of $ 500 paid at the end of each month of the calendar years for one year. The annual interest rate is 12 %.

i – Frequency of occurrences

Present value Annuity Factor

r – Discount raten – the time period in years

For the sake of simplicity and ease of using financial models, professionals usually calculate present value annuity factors, which helps them to keep an eye on discount rates as well as total annuity factors.

This factor is maintained into tabular forms to find out the present value per dollar of cash flow based on the periods and the discount rate period. Once the value of dollar cash flows is known, the actual period cash flows are multiplied by the annuity factor to find out the present value of the annuity.

Calculate Present Value of an Annuity Due

Until now, we have seen annuity payment done at the end of each period. What if payment is made at the starting of the period, then the above formula will misguide us. Annuity due formula can help us in finding out the present value of annuity whose payment is made at the starting date of the period.

p – Equated annual paymentsr – Discount raten – the time period in years

Present Value Of An Annuity Definition Interpretation