Get a Grasp of the Present Value of an Annuity

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.

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.

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.

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 products, 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.

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