# The time value of money

One of the most important principles of **personal finance** is that money has a time value associated with it. A dollar received today is worth more than a dollar received in the future. This is because by investing the dollar you received today, you start earning interest on it. As mentioned in the post “The three key investing variables”, the longer the time frame of your investment program, the greater the power of compound interest.

Because of the time value associated with money, you cannot compare amounts of money from two different periods of time without first adjusting their values. Having a good understanding of the time value of money will allow you to understand how an investment grows over time.

### Calculating the future value of an investment

In order to determine how much an investment will be worth in the future you would need to calculate the future value (FV) of the investment using the following formula:

FV_{n} = PV (1 + i)^{n}

where

PV = the present value (current value) of a sum of money

i = the annual interest rate earned

n = the number of years that the compounding occurs

So for example, if you deposit $500 in a savings account which pays 4% interest annually, how much would it be worth in 5 years?

By applying the future value formula we can see that

FV = $500 (1 + 0.4)^{5}

= $500 (1.217)

= $608.50

### The rule of 72

What if you would simply like to approximate how long it would take you to double your investment? You can use the rule of 72. All you have to do is divide the annual interest into 72. So for example, it would take 18 years to double the $500 invested in the savings account considering a 4% annual interest (72/4 = 18 years).

### Calculating the present value of an investment

What if instead of calculating the future value of an investment we wanted to determine how much a sum of money to be received in the future is worth in today’s dollars? What is the present value of such sum of money? Calculating the present value (PV) of an investment is important because it adjusts it to inflation. Recall that both future value and present value must be used in order to adjust sums of money in order to compare investments from different time periods. When calculating the present value we are simply bringing future money back to present. This is done by using a discount rate. The discount rate is the interest rate used to “discount” the future money back to present. The present value formula is simply the inverse of the future value formula.

PV = FV_{n} = the future value of the investment after n years

i = the annual discount rate (interest rate)

n = number of years after which the payment will be received