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Annuity Table

Annuity Table

What Is an Annuity Table?

An annuity table is an instrument for deciding the present value of an annuity or other structured series of payments. Such an instrument, utilized by accountants, actuaries, and other insurance faculty, considers how much money has been set into an annuity and how long it has been there to decide how much money would be due to an annuity buyer or annuitant.

Calculating the current value of any future amount of an annuity may likewise be performed utilizing a financial calculator or software worked for such a purpose.

How an Annuity Table Works

An annuity table gives a factor, in view of time, and a discount rate (interest rate) by which an annuity payment can be duplicated to decide its current value. For instance, an annuity table could be utilized to work out the present value of an annuity that paid $10,000 per year for quite some time assuming the interest rate is expected to be 3%.

As per the concept of the time value of money, getting a lump sum payment in the present is worth more than getting a similar sum from here on out. Accordingly, having $10,000 today is better than being given $1,000 each year for the next 10 years on the grounds that the sum could be invested and earn interest over that decade. Toward the finish of the 10-year period, the $10,000 lump sum would be worth more than the sum of the annual payments, even whenever invested at a similar interest rate.

Annuity Table Uses

A lottery victor could utilize an annuity table to decide if it checks out to accept his lottery rewards as a lump-sum payment today or as a series of payments over numerous years. Lottery rewards are a rare form of an annuity. All the more normally, annuities are a type of investment used to give individuals a consistent income in retirement.

Annuity Table and the Present Value of an Annuity

Present Value of an Annuity Formulas

The formula for the current value of a ordinary annuity, instead of a annuity due, is as per the following:
P=PMT√ó1‚ąí(1+r)‚ąínrwhere:P=Present¬†value¬†of¬†an¬†annuity¬†streamPMT=Dollar¬†amount¬†of¬†each¬†annuity¬†paymentr=Interest¬†rate¬†(also¬†known¬†as¬†the¬†discount¬†rate)n=Number¬†of¬†periods¬†in¬†which¬†payments¬†will¬†be¬†made\begin&\text =\text\times\frac{ 1 - (1 + r) ^ -n}\&\textbf\&\text = \text\&\text =\text\&r = \text{Interest rate (also known as the discount rate)}\&n = \text\end
Assume an individual has an opportunity to receive an annuity that pays $50,000 each year for the next 25 years, with a discount rate of 6%, or a lump sum payment of $650,000. He wants to decide the more rational option. Utilizing the above formula, the current value of this annuity is:
PVA=$50,000√ó1‚ąí(1+0.06)‚ąí250.06=$639,168where:PVA=Present¬†value¬†of¬†annuity\begin&\text = $50,000 \times \frac{1 - (1 + 0.06) ^ -25}{0.06} = $639,168\&\textbf\&\text=\text\end
Given this information, the annuity is worth $10,832 less on a period changed basis, and the individual ought to pick the lump sum payment over the annuity.

Note, this formula is for an ordinary annuity where payments are made toward the finish of the period being referred to. In the above model, each $50,000 payment would happen toward the year's end, every year, for a long time. With an annuity due, the payments are made toward the beginning of the period being referred to. To track down the value of an annuity due, basically increase the above formula by a factor of (1 + r):
P=PMT√ó(1‚ąí(1+r)‚ąínr)√ó(1+r)\begin&\text = \text \times\left(\frac{1 - (1 + r) ^ -n}\right) \times (1 + r)\end
On the off chance that the above illustration of an annuity due, its value would be:
P=$50,000√ó(1‚ąí(1+0.06)‚ąí250.06)√ó(1+0.06)=$677,518\begin&\text= $50,000\&\quad \times\left( \frac{1 - (1 + 0.06) ^ -25}{0.06}\right)\times (1 + 0.06) = $677,518\end
In this case, the individual ought to pick the annuity due, on the grounds that it is worth $27,518 more than the lump sum payment.

Present Value of an Annuity Table

As opposed to working through the formulas above, you could on the other hand utilize an annuity table. An annuity table improves on the math via consequently giving you a factor for the last part of the formula above. For instance, the current value of an ordinary annuity table would give you one number (alluded to as a factor) that is pre-determined for the (1 - (1 + r) ^ - n)/r) portion of the formula.

The still up in the air by the interest rate (r in the formula) and the number of periods wherein payments will be made (n in the formula). In an annuity table, the number of periods is generally portrayed down the left column. The interest rate is normally portrayed across the top line. Basically select the right interest rate and number of periods to track down your factor in the crossing cell. That factor is then increased by the dollar amount of the annuity payment to show up at the current value of the ordinary annuity.

Below is an illustration of a current value of an ordinary annuity table:

n1%2%3%4%5%6%
10.99010.98040.97090.96150.95240.9434
21.97041.94161.91351.88611.85941.8334
32.94102.88392.82862.77512.72332.6730
43.90203.80773.71713.62993.54603.4651
54.85344.71354.57974.45184.32954.2124
109.47138.98268.53028.11097.72177.3601
1513.865112.849311.938011.118410.37979.7123
2018.045616.351414.877513.590312.462211.4699
2522.023219.523517.413215.622114.093912.7834
In the event that we take the model above with a 6% interest rate and a 25 year period, you will track down the factor = 12.7834. Assuming that you duplicate this 12.7834 factor from the annuity table by the $50,000 payment amount, you will get $639,168. Notice, this is equivalent to the aftereffect of the formula above.

There is a separate table for the current value of an annuity due, and it will give you the right factor in view of the subsequent formula.

Features

  • Utilizing an annuity table, you will duplicate the dollar amount of your recurring payment by the given factor.
  • An annuity table computes the current value of an annuity utilizing a formula that applies a discount rate to future payments.
  • An annuity table is a device used to decide the current value of an annuity.
  • An annuity table purposes the discount rate and number of period for payment to give you a fitting factor.