Present Value of Ordinary Annuity
The present value of an ordinary annuity refers to the current worth of a stream of equal payments expected in the future, discounted back to the present at a specific rate of return (or discount rate). This calculation assumes the payments are made at the end of each period (which is why it’s referred to as “ordinary”).
An ordinary annuity is a series of equal payments made at regular intervals. For instance, monthly rent payments, annual scholarship payments, and quarterly dividends can all be examples of ordinary annuities.
The formula to calculate the present value of an ordinary annuity is:
PV = Pmt * [1 – (1 + r)^-n] / r
Where:
- PV is the present value of the annuity
- Pmt is the amount of each equal payment
- r is the discount rate per period
- n is the number of periods
This formula allows us to answer questions like “how much money would I need in the bank today, in order to generate a series of $500 payments for the next 10 years, given a yearly interest rate of 5%?
Remember, this formula assumes the payments occur at the end of each period. If the payments occur at the beginning of each period (also known as an annuity due), the formula needs to be adjusted accordingly.
Example of the Present Value of Ordinary Annuity
Imagine you are going to receive $1,000 per year for the next 6 years and you want to know what that stream of payments is worth in today’s dollars. Let’s say the discount rate (the rate of return you could earn on a similar investment) is 4%.
We can calculate the present value of this ordinary annuity using the formula:
PV = Pmt * [1 – (1 + r)^-n] / r
Substituting the given values into the formula:
PV = $1,000 * [1 – (1 + 0.04)^-6] / 0.04
Perform the calculation:
PV = $1,000 * [1 – 0.79032] / 0.04
So:
PV = $1,000 * 0.20968 / 0.04
Therefore:
PV = $5,242
So, the present value of receiving $1,000 per year for the next 6 years, discounted at an annual rate of 4%, is approximately $5,242. This is the amount you’d be indifferent to receiving today versus receiving $1,000 per year for the next 6 years, assuming you could earn 4% per year on the money.
