Present Value of an Ordinary Annuity Table [With Simple Examples]
What is a Present Value of an Ordinary Annuity Table?
A Present Value of an Ordinary Annuity Table is a financial tool used to calculate the present value of an ordinary annuity.
Let’s now cover what the terms present value and annuity actually mean.
Present Value
Present value (PV) is the current worth of future money, adjusted for a specific interest rate.
It is based on the idea that money today is worth more than the same amount in the future, due to its potential earning capacity.
Imagine you have the option to receive £1,000 today or £1,000 one year from now.
Most people would prefer to have the money now as they would be able to invest it and earn interest over the year.
If we could get a 5% interest rate, then £1,000 received one year from now is not worth £1,000 today.
Therefore, the present value is lower because we would discount the £1,000 by the interest rate.
The Present Value formula is:
PV = FV / [(1+r)n]
Where:
PV = The present value
FV = Future Value
r = The discount rate (or interest rate)
n = The number of periods
In the example above, we can work out what the present value of £1,000 would be at a 5% interest rate:
PV = FV / [(1+r)n]
PV = £1,000 / [(1+0.05)1]
PV = £1,000 / [(1.05)1]
PV = £1,000 / 1.05
PV = £952.38
So, £1,000 one year from now is worth £952.38 today at a 5% interest rate.
Annuity
An annuity is a financial product that provides regular payments over a period of time.
For example, when a bank provides a mortgage to a customer, the customer will make regular payments to the bank for a set period of time.
There are two types of annuities:
- Ordinary Annuity: Payments are made at the end of each period. For example, receiving rent payments at the end of each month.
- Annuity Due: Payments are made at the beginning of each period. For example, paying rent at the start of each month.
Formula for Calculating the Present Value of an Ordinary Annuity
The formula for calculating the present value of an ordinary annuity is:
PV = PMT [(1 – (1 + r)-n)) / r]
Where:
PV = The present value of the annuity
PMT = The amount of each annuity payment
r = The discount rate (or interest rate)
n = The number of periods over which payments are made
Rate Table For the Present Value of an Ordinary Annuity of 1
Cumulative Rate Table For the Present Value of an Ordinary Annuity of 1
Example of Calculating the Present Value of an Ordinary Annuity
So how would we find the present value of an ordinary annuity that pays £1,000 annually for 5 years, at a discount rate of 6%?
First of all, we would find the column with the 6% discount rate.
Then we would find the row for 5 periods.
Now we would find the intersection of the 6% column and the 5 periods row to get the factor:
So the factor is 4.212
Now we can multiply the periodic payment (£1,000) by the factor from the table.
Present Value = £1,000 x 4.212
Present Value = 4,212
This can also be calculated using the Formula for Calculating the Present Value of an Ordinary Annuity:
PV = PMT [(1 – (1 + r)-n)) / r]
Annuity Payment | PMT | £1,000 |
Interest Rate | R | 6% (or 0.06 as a decimal) |
Number of Periods | n | 5 |
PV = PMT [(1 – (1 + r)-n)) / r]
PV = £1,000 [(1 – (1 + 0.06)-5)) / 0.06]
PV = £1,000 [(1 – (1.06)-5)) / 0.06]
PV = £1,000 [(1 – (0.7472581728)) / 0.06]
PV = £1,000 [0.2527418272 / 0.06]
PV = £1,000 [4.2123637866]
PV = £4,212.36