Present Value (PV)

Money now is more valuable than money later on.

Why? Because you can use money to make more money!

You could run a business, or buy something now and sell it later for more, or simply put the money in the bank to earn interest.

Example: You can get 10% interest on your money.

So $1,000 now can earn $1,000 x 10% = $100 in a year.

Your $1,000 now can become $1,100 in a year's time.

Present Value

Present value of $1,000 today compared to a future value of $1,100 in one year at 10% interest
So $1,000 now is the same as $1,100 next year (at 10% interest).
A small stack of coins growing into a taller stack of coins over time

We say the Present Value of $1,100 next year is $1,000

Because we could turn $1,000 into $1,100 (if we could earn 10% interest).

Now let's extend this idea further into the future ...

How to Calculate Future Payments

Let's stay with 10% Interest. That means that money grows by 10% every year, like this:

Flowchart showing $1,000 earning 10% interest to become $1,100, then $1,210, and then $1,331

So:

$1,100 next year is the same as $1,000 now
And $1,210 in 2 years is the same as $1,000 now
and so on

In fact all those amounts are the same (considering when they occur and the 10% interest).

Easier Calculation

But instead of "adding 10%" to each year it is easier to multiply by 1.10 (explained at Compound Interest):

Diagram showing that adding 10% is mathematically equivalent to multiplying by 1.10

So we get this (same result as above):

To convert the interest rate to a multiplier: turn the percentage into a decimal and add 1. Examples:

6% becomes 0.06 as a decimal, then add 1 to get 1.06
14% becomes 0.14 as a decimal, then add 1 to get 1.14
0.5% (half a percent) becomes 0.005 as a decimal, then add 1 to get 1.005

Future Back to Now

And to see what money in the future is worth now, go backwards (dividing by 1.10 each year instead of multiplying):

Example: Sam promises you $500 next year, what's the Present Value?

To take a future payment backwards one year divide by 1.10

So $500 next year is $500 ÷ 1.10 = $454.55 now (to nearest cent).

The Present Value is $454.55

Example: Alex promises you $900 in 3 years, what's the Present Value?

To take a future payment backwards three years divide by 1.10 three times

So $900 in 3 years is:

$900 ÷ 1.10 ÷ 1.10 ÷ 1.10

$900 ÷ (1.10 × 1.10 × 1.10)

$900 ÷ 1.331

$676.18 now (to nearest cent).

Better With Exponents

But instead of $900 ÷ (1.10 × 1.10 × 1.10) it is better to use exponents (the exponent says how many times to use the number in a multiplication).

Example: (continued)

The Present Value of $900 in 3 years (in one go):

$900 ÷ 1.10³ = $676.18 now (to nearest cent).

As a formula it is:

PV = FV / (1+r)ⁿ

PV is Present Value
FV is Future Value
r is the interest rate (as a decimal, so 0.10, not 10%)
n is the number of years

Example: (continued)

Use the formula to calculate Present Value of $900 in 3 years:

PV = FV / (1+r)ⁿ

PV = $900 / (1 + 0.10)³ = $900 / 1.10³ = $676.18 (to nearest cent).

Calculator key showing the exponent function x to the power of y

Exponents are easier to use, particularly with a calculator.

For example 1.10⁶ is quicker than 1.10 × 1.10 × 1.10 × 1.10 × 1.10 × 1.10

Let's use the formula a little more:

Example: What's $570 next year worth now, at an interest rate of 10% ?

PV = $570 / (1+0.10)¹ = $570 / 1.10 = $518.18 (to nearest cent)

But your choice of interest rate can change things!

Example: What's $570 next year worth now, at an interest rate of 15% ?

PV = $570 / (1+0.15)¹ = $570 / 1.15 = $495.65 (to nearest cent)

Or what if you don't get the money for 3 years

Example: What's $570 in 3 years worth now, at an interest rate of 10% ?

PV = $570 / (1+0.10)³ = $570 / 1.331 = $428.25 (to nearest cent)

One last example:

Example: You are promised $800 in 10 years time. What's its Present Value at an interest rate of 6% ?

PV = $800 / (1+0.06)¹⁰ = $800 / 1.7908... = $446.72 (to nearest cent)