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Present Value of an Annuity: Formula, Examples & How to Calculate

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Get a Grasp of the Present Value of an Annuity
February 23, 2023

Table of Content

 

What is the Present Value of an Annuity?

Current values of any future payments that arise from an annuity means the “present value of an annuity”. Future payments that may be generated out of an annuity arise due to certain applicable rates of return. These are also called “discount rates”. When discount rates are high, the present annuity value gets lowered. PV or present value is a crucial calculation, relying on the idea of the value of time of money. This means that a rupee at the current time is comparatively more valuable, in terms of its purchasing power, than a rupee will be at any future date.

Due to the time value that refers to money, the money that is acquired today stands to be worth much more relative to the identical amount of money at any future date. Why is this case? This is because, in the meantime, the money can be invested. Using this rationale, Rs. 10,000 at present is worth above Rs. 10,000 spread across ten annual installments of Rs.1, 000 for each installment.

Why is the present value of the annuity important?

The present value of annuity is the total cash value of the future annuity payments at a given discount rate. Once you get that figure, you will be in a position to understand how much value your retirement plan will generate if you receive the maturity benefit as an annuity payment spread over a defined period or your entire lifetime. Comparing that amount with the lump sum payable at maturity, it will be easier to decide whether taking the maturity benefit as a single payment or through annuities is profitable for your retirement goals. This is where the importance of the present value of annuity lies. 

Present Value and the Discount Rate

The present value of an annuity is a vital concept in terms of annuities as it permits people to compare values while receiving a stream of payments at a future date to values of gaining lump sums in the present time. If you calculate the present value of an annuity, you can determine the benefit of getting a payment as a lump sum or receiving an annuity which is spread over a period (across years). It is crucial when you make certain financial decisions, for instance, whether to choose a lump sum out of a pension scheme or get a flow of installments instead. Calculations of the present value of an annuity can additionally be made use of in comparisons of various options of annuity concerning their value. Annuities may have distinctive payment amounts and varying schedules of payment.

Once you have a good background of the concepts in terms of the annuity and its payments, you will get a good grasp of the “discount rate”. A significant factor in calculating the present value of an annuity is the discount rate. Put simply, the discount rate refers to an assumed return rate, or a rate of interest, used to find out the current value of payments of the future. What the discount rate accounts for is money’s time value. Essentially, the meaning of this is that a rupee today has more worth than a rupee at a future date because it may be invested to earn returns. If the discount rate is high, the present value of an annuity is low, as payments in the future are discounted strongly.

Relationship between Interest Rates and the Time Value of Money

The present value of annuity formula takes into account the rate of return or discount rate which is not the interest rate, but the time value of money. To get clarity on the concept, it’s crucial to understand the relationship between interest rates and the time value of money, based on their definitions. Going by the rule of economics, the value of money depreciates with time. Hence, the value of Rs 5000 today is higher than that of Rs 5000 a decade later. Here the time value of money equals the difference between the present worth and the promised future worth of the same amount. Whereas, rate of interest refers to the amount you receive as a return earned on your investment and reflects the cost of borrowing. 

So, how does the relationship between the two matters?

To choose between a lump sum or annuity payment, it’s crucial to understand which will fetch you a higher gain. Here, you can calculate the present value of annuity considering the time value of money and the amount that can be earned by reinvesting the lumpsum for the same period at a specified rate of interest. The one that yields a bigger value should be your option to redeem the maturity benefit of your investment. 

Formula and Calculation of the Present Value of an Annuity

The formula to calculate the present value of an annuity is shown below:

P = PMT x 1 - (1 / 1+r) raised to n divided by r

Here: P = the present value of a stream of annuity

PMT = the rupee amount of every annuity payment

r= discount rate or interest rate

n= installments in which payments are due to be made

Example of the Present Value of an Annuity

Say an individual gets a chance to get an annuity which pays out Rs. 55,000 a year. This is valid for 25 years. The discount rate is fixed at 6%. The individual also has the option of taking Rs. 6, 50,000 as a payment in a lump sum. Which of these do you think is the more lucrative option? If you calculate with the formula mentioned above, the annuity works out less over a time frame, to around Rs. 10, 832 lower. In this case, the lump sum option would be better.

Using an online calculator for the present value of annuity

To calculate the present value of annuity for your financial planning, you can always seek help from financial advisors. But these days, many financial and investment websites have an online calculator option, that lets you do the estimation yourself. Such a retirement calculator equips you to arrive at the current value of the promised future annuity payments, based on the time value of money and some inputs from your end. 

To calculate the PV of annuity by using an online calculator, you need to provide the following information. 

  • Payment type
  • Payment schedule
  • Frequency of payment
  • Worth of each payment
  • Number of payments due

However, it’s important to note here that online calculators may or may not be accurate. In real-life calculations, secondary market buyers can consider a unique combination of variables for each customer, whereas online estimations are generic. This unique set includes

  • Current annuity market rates
  • Amount of money left in the annuity
  • Start of the annuity schedule
  • Specific company guidelines
  • Fees and other charges

In addition, the calculations of the online calculator can also vary if the annuity plan follows fluctuating interest rates contributing to market value of adjustment or increasing payment options. 

When is the present value of annuity calculated?

The calculation of the present value of annuity is required majorly to estimate the cash value of retirement benefits, loans and recurring payments in court settlements. It is also essential in figuring out if the mortgage value is higher than its expected value. These payments are sometimes considered annuities. 

Understanding annuities

Annuity is an investment plan that offers you a regular income stream for a defined period or a lifetime in exchange for premiums paid earlier. A financial contract between you and the insurance company, annuity is ideally designed for the retirement period to ensure an alternative source of income when salary is no longer available. 

Those who purchase these plans pay a premium till their retirement which gets converted into the annuity payment afterwards. They can then decide whether the premiums should be invested and in which market-linked instruments they should be invested in to fetch good returns. Typically, the following are the variants of an annuity contract:

Fixed annuities: Pays guaranteed interests over a certain period.

Variable annuities: The annuities payable keep varying based on the returns from the funds chosen for the investment of the premiums. The higher the return earned, the bigger will be the annuity amount and vice versa. 

Indexed annuities: This is a hybrid annuity of fixed and variable components. Indexed annuities follow a stock market index like the Dow Jones Industrial Average or the S&P 500 and pay out a percentage of the return. 

Another crucial thing that you need to remember is, that though premiums for the annuity plans are not taxed, the earnings are subject to regular tax rates. So, annuity plans are tax-deferred. 

Factors affecting the present value of an annuity

The present value of annuity can be governed by certain factors. Most of these cater to the annuity contract like the interest rates, payouts and time to maturity. However, a few other things affect the PV of annuity strongly, the most important of which is inflation. Here’s a look at the factors that contribute to the estimation of the present value. 

- Interest rate: The annuity interest rate is the discount rate that is applied to future payments to arrive at their present worth. The higher this rate, the lower will be the present value. 

- Time to maturity: This refers to the time till the plan starts paying annuities. Until then, the premium paid towards the plan fetches compound interests that accrue into the annuity. So longer the time to maturity, the bigger the build-up of compound interests leading to higher PV of annuities.   

- Payment and its frequency: The present value of annuity is the future payment converted to its present worth. So, the higher the number of payments and the bigger their value, the greater the estimated present value.

- Inflation: Inflation can cause the purchasing power of money to fall over time. This leads to the lower present value of an annuity. 

Annuity vs. Annuity Due

The difference between an annuity and an “annuity due” is in terms of when payments are made. The annuity’s payments are made at the end of a period of time. In the case of an annuity due, the payments are made at the start of a period. The annuity due will, thus, be more valuable at the current time. When the option of annuity due is available, this usually works out to more than the lump sum payment option.

Why is Future Value (FV) Important to Investors?

The value reflecting a present asset in the future is the “future value” or FV. The FV is according to an estimated growth rate. This is important to investors who wish to predict how much of an investment they make in the present day will be of value at a date in a future time. In addition, this acts as an aid for investors to make sound decisions where investments are concerned, according to requirements and personal goals.

How Does an Ordinary Annuity Differ From an Annuity Due?

  • What Is the Formula for the Present Value of an Ordinary Annuity?

    • The formula of the present value of an annuity, or an ordinary annuity, shows below:

    P = PMT x 1 - (1 / l + r raised to n) divided by r

    Here:

    P is the present value of a stream of annuity

    PMT is the rupee amount of every annuity installment

    r= the discount rate or rate of interest

    n= the installments in which payments are due to be made

  • What Is the Formula for the Present Value of an Annuity Due?

    • Payments in an annuity due are made at the start of every period, so the formula becomes different relative to the formula of an annuity or an ordinary annuity. For an annuity due, you have to multiply the formula mentioned for the ordinary annuity by (1+r), so the formula is:

    P = PMT x 1 - (1 / l + r raised to n) divided by r multiplied by 1+r

  • The Bottom Line

    • While you invest in instruments like life insurance plans, you may have the option to receive payments as lump sums or in installments based on your premiums. In case you wish to decide on which is best for you, it is vital to know specific terms and how formulas work to calculate amounts, giving you the benefits you require.

FAQs on the present value of an annuity

Q: How reliable are annuity calculators available online?

The annuity calculator available online do not have access to the unique combination of variables catering to each customer, set by secondary market buyers. Hence, the outputs can differ from the results of applying the present value of annuity formula. 

Q: What is the formula for the present value annuity factor?

The formula for present value annuity is 

PV = PMT x [1-{1/(1+r)n}/r]

Here PV stands for Present value, PMT is the amount of each annuity, r equals the annuity interest rate or discount rate and n refers to the number of periods for which the annuity is payable.  

Q: What is the present and future value of an annuity?

The future value of an annuity is the total cash flow of a promised amount of periodic payouts for a definite or indefinite time frame. Whereas, the present value of the annuity refers to the present worth of all the future payments taken together taking into account the discount rate. Here the discount rate is the time value of money by which the same amount gets reduced in worth over time. 

Q: What is the present value of the annuity table?

The annuity table is a representation of the present value of annuity. It contains a factor associated with the number of payments, based on which you expect the future flow of annuities, a series of equal payments over a certain period at a specific discount rate. Multiplying this factor by one of the payments, you can get the present value of the annuity stream.      

Q: What is an example scenario for calculating the present value of an annuity?

An example scenario for calculating the present value of annuity can be a retirement plan which offers its maturity benefit either as a lump sum of Rs 6 lakh or an annuity stream offering Rs 50,000 per annum for 25 years at a 6% discount rate. 

Applying the formula, the present value of the annuity will be:

PV = Rs 50000 x [1-{1/(1+0.06)25}/0.06]

     = Rs 6,39,168

Since the present value of the annuity is more than Rs 6 lakh, here the annuity option will be more profitable than the lump sum payment.

Related Article 

ARN – ED/02/24/8895

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Francis Rodrigues Francis Rodrigues

Francis Rodrigues has a decade long experience in the insurance sector, and as SVP, E-Commerce and Digital Marketing, HDFC Life, manages the online sales channel, as well as digital and performance marketing. He has had hands-on experience in setting up sales channels and functional teams from scratch over a career spanning 2 decades.

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