Annuity Formula

The Present Value of Regular Payments

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

The Present Value of Regular Payments:

mr annuity toad
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:

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.

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