# 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

So $1,000 now is the **same** as $1,100 next year (at 10% interest).

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 us extend this idea further into the future ...

## How to Calculate Future Payments

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

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**. - etc

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):

So we get this (same result as above):

## 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 is the Present Value?

**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 is the Present Value?

**divide by 1.10**three times

So **$900 in 3 years** is:

**$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):

^{3}=

**$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**:

^{n}

^{3}= $900 / 1.10

^{3}=

**$676.18**(to nearest cent).

Exponents are easier to use, particularly with a calculator. For example 1.10 |

Let us use the formula a little more:

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

^{1}= $570 / 1.10 =

**$518.18**(to nearest cent)

But your choice of interest rate can change things!

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

^{1}= $570 / 1.15 =

**$495.65**(to nearest cent)

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

### Example: What is $570 in 3 years time worth now, at an interest rate of 10% ?

^{3}= $570 / 1.331 =

**$428.25**(to nearest cent)

One last example:

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

^{10}= $800 / 1.7908... =

**$446.72**(to nearest cent)