Present Value (PV) (2024)

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?

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 is 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).

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).

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 us use the formula a little more:

Example: What is $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 is $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 is $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 is its Present Value at an interest rate of 6% ?

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

Investing (Introduction) Investment/Loan Graph Net Present Value Money Index

As an enthusiast with a deep understanding of financial concepts, let's delve into the key concepts covered in the provided article.

Time Value of Money: The article begins by asserting that money now is more valuable than money later due to its potential to generate additional wealth over time. This idea is rooted in the concept of the time value of money, a fundamental principle in finance.

Opportunity for Growth: The article introduces the idea that money can be used to make more money, whether through running a business, buying and selling assets, or earning interest in a bank. This highlights the potential for wealth accumulation and the various avenues available for financial growth.

Present Value: The concept of present value is crucial in understanding the article. It's explained that the present value of a future amount of money is the amount you would need to have today to equal that future amount, given a specific interest rate. In the example, $1,000 now is considered equivalent to $1,100 next year with a 10% interest rate.

Future Value and Compound Interest: The article then extends the idea into the future, illustrating how future amounts can be calculated based on a given interest rate. It introduces the concept of compound interest, explaining that instead of adding a percentage each year, it is more convenient to multiply by a factor (1 + interest rate).

Calculating Present Value: The article provides a step-by-step guide on how to calculate the present value of a future amount using the formula PV = FV / (1+r)^n, where PV is the present value, FV is the future value, r is the interest rate (in decimal form), and n is the number of years.

Exponential Notation: The use of exponents is introduced as a more efficient way to express repeated multiplication in the context of calculating present value. The formula is simplified to PV = FV / (1+r)^n, emphasizing the power of exponents for more straightforward calculations.

Effect of Interest Rate: The article demonstrates how the choice of interest rate can significantly impact the present value of a future amount. Different interest rates result in different present values, highlighting the importance of considering interest rates in financial calculations.

Practical Examples: Several examples are provided to illustrate the application of the present value formula in real scenarios. These examples involve calculating the present value of future amounts given specific interest rates and time periods.

By understanding these concepts, individuals can make informed financial decisions, considering the time value of money and the potential for growth through strategic investments and financial planning.