Time Value of Money

I've been cautious about being overly technical in my posts, so far. For the most part I'll hold true to that approach. However, today I'm going to introduce the most important technical concept we need to build wealth, time value of money (TVM). Those who understand it build wealth.

Today's post is a primer I will refer back to in future posts. We'll use it for a variety of things like calculating a mortgage payment, calculating the cost of paying interest on a credit card, determining how much we'll save over a period of years, and many other things.

The importance of TVM for each of us is related to our borrowing, saving, and investing money. Basically, $1.00 today is worth more than $1.00 in the future.

The TVM is the value of money given an interest rate and an amount of time.

A simple example of time value of money is you save $1 today for one year, at 6% interest, and you'll receive $1.06 one year from today. $1.00 of what you get back was yours already and the bank paid you $0.06 to borrow your money for a year.

NOTE: If you put this example into a financial calculator, the answer to your future value will be $-1.06. The reason it will show negative is at the beginning of the year you gave money to the bank, at the end they gave it back. The negative number denotes one of the cash flows is away from you while the other is to you.

Time value of money has five variables, one of which you'll solve for each time you use this tool.

1. Present Value (PV) is the value of a future stream of income today. If you have $100 in the bank right now, the present value is $100. If you need $100,000 in 20 years, you could calculate how much (the PV) you would need today for it to grow to $100,000 over 20 years.
2. Rate (i) is the percentage you will pay to use someone else's money in a loan. Even better, rate is the percentage someone else will pay you to use your money. The symbol for Rate is i because rate means Interest Rate. Most rates are published as annual percentage rates. If you are calculating the present value of a set of monthly payments you should divide the APR by 12, an annual payment you would use the APR, etc. Make sure you are using the APR or interest rate and not the annual percentage yield (APY). I'll cover the difference in a future post. For now, use the APR.
3. Periods (n) is the number of years, months, etc you will leave your money in an investment or will receive / make a payment. A 30 year mortgage has 360 (30 years x 12 months) periods or payments.
4. Future Value (FV) is the value of today's investment after it has grown from interest or your additional investments. We'll use future value calculations to determine the size of your nest egg when you retire.
5. Payment (PMT) is the payment you'll make or amount you'll save per period.

The primary TVM formula is below. As you can imagine, there are dozens of derivatives. I give this to you as a reference only. Don't don't worry about studying it. The most important thing to understand is that the formula is the same whether you are borrowing or saving money. You'll use the same calculator in either case.

If you're a math lover, have a blast. As much as I like math, I prefer a financial calculator to solve for any of the five variables. If you don't own financial calculator (not the same as a scientific calculator), here is a free online one.

Understanding time value of money is critical to building wealth. I'd suggest using the calculator above to run through a couple of your scenarios. It'll help this concept resonate better.

I've run through a sample auto loan below. As you can see, the PV is the amount borrowed. The Rate is the monthly interest paid. I've used an annual percentage of 6%, which makes .5% per month. The number of periods (n) is the number of months my loan is for. FV is zero since when I finish the 60 months, I won't owe anything to the bank. Then I clicked on PMT to calculate my monthly payment. As you can see, it's negative to denote I'm paying the bank.

TVM of money is a somewhat difficult concept, but it's a critical thing to understand to help you build wealth. I know this post reads like a text book, so if you have questions post them. We'll work through them together.