Time Value of money

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So what is worth more a dollar today or a dollar tomorrow? It seems like a dollar should be a dollar, why would it change from day to day? The thing is that it does, maybe not noticeable in a day - but dollars have this interesting thing they can do, they can be invested and propagate. This is what the time part of the title refers to. Over time that dollar gets more and more valuable.

The question though is how valuable is that dollar? Well that depends, it depends on what you can use that dollar for and we might bust out a spread sheet and see how much money that dollar would be worth at a specific rate of return.

This can be express mathematically by the formula FV = PV x[1+i/n] ^ (n x t)

FV = Future value of money
PV = Present value of money
n = number of compounding periods per year
t = number of years

This typically is consolidated down to FV = PV (1+ i) ^ t because we humans are lazy and only consider compounding happening once a year.

This can be used in many ways but for personal finance typically what I've used it for is figuring out how expensive something really is. 

Let's say your looking at a dresser, the one that you want is 500 dollars brand spanking new from Cost Co. The other option is a slightly beat up 45 bucks ok-ish dresser (that we will round to 50 for the blog) that might last 5 - 10 years.

It seems like we should just buy the 500 dollar one, in 5 years we will have to any way and now it's going to be 550 bucks that we spent in total. The thing is that those 500 bucks can be used now on other things. Specifically they can be used to pay off debts. Your highest interest rate is the one you would want to use.

If you have credit card debt than the interest rate you will be using is around 15% in fact it is exactly the amount of interest your paying on that credit card debt because you could have been using that dollar to pay off the debt. 

FV = 450 (1+.15)^5 = 905.11

So if we hold off on that purchase and get something that satisfies our immediate needs we can buy the item we really want in 5 years and have 400 bucks left over.

If you don't have any debt than a good rate is the Safe Withdrawal Rate - 4%

FV = 450  (1+.04)^5 = 547.49

So if we hold off on the purchase we can buy that lesser dresser and keep buying it every 5 years and have 500 bucks lying around in case of an emergency or more if the dresser lasts longer than 5 years.

Now that doesn't mean you shouldn't buy that 500 dollar dresser but you should know that dresser isn't costing you 500 bucks, it's costing significantly more. If you expect to live to 80 than how much that 500 bucks is really worth will depend on how old you are.

at 4% interest rate

Age                  Time Value of Money

20	4733.83
30	3198.01
40	2160.46
50	1459.53
60	986.01
70	666.11

So if your youngish that dresser is going to cost you a significant amount of money. The older you get the cheaper it is. That is power of the Time Value of Money.