# The Present Value of Regular Payments

On the Annuity Formula homepage, we used the following example to introduce:

Q. Mr Toad is very lucky. He is going to receive regular payments of $1000 at the end of each year for five years.
With no inflation, the $5000 he receives in total will be worth $5000 in five years' time.
If, however, inflation runs at 4% a year for five years, how much will the $5000 be worth at today's value?

A. The value of the payments today is $4451.82.

This was calculated using the following annuity formula:

• We wish to calculate

•

•

•

We now put these numbers into the equation and find:

Therefore

Now here's a practice question for you:

Q. Which is worth more in today's money?

Option 1. 10 annual payments of $1000 with annual inflation of 10%?

Option 2. 10 annual payments of $900 with annual inflation at 5%?

Try doing the calculation yourself, then scroll down to check your answer at the bottom of the page.

A. After 10 years, we find Option 1 is worth $6144.57 and Option 2 is worth $6949.56. In this case the $900 annuity payments are cumulatively worth more than the $1000 payments, because the value of the $900 payments is not eroded as much by inflation.

**The Present Value of Regular Payments**:

A. The value of the payments today is $4451.82.

This was calculated using the following annuity formula:

**Using the annuity formula to answer the question:**

• We wish to calculate

**PV**, the present value •

•

**RP**, the regular payment, is $1000 •

•

**i**, the inflation rate, is 4%, which we write as 0.04 •

•

**n**, the number of payments, is 5 •

We now put these numbers into the equation and find:

**PV**= 1000 x [1 - (1 + 0.04)

^{-5}]/0.04

Therefore

**PV**= 1000 x [1 - 0.821927]/0.04

**Hence PV = $4451.82**

Now here's a practice question for you:

Q. Which is worth more in today's money?

Option 1. 10 annual payments of $1000 with annual inflation of 10%?

Option 2. 10 annual payments of $900 with annual inflation at 5%?

Try doing the calculation yourself, then scroll down to check your answer at the bottom of the page.

A. After 10 years, we find Option 1 is worth $6144.57 and Option 2 is worth $6949.56. In this case the $900 annuity payments are cumulatively worth more than the $1000 payments, because the value of the $900 payments is not eroded as much by inflation.