 So we have discussed a bit about returns and rates, but there is some terminology that needs to be addressed and will make you a bit better off for knowing it. At the end of the day interest rates are pretty powerful things that shape the entire financial system, so let’s learn a little more about them. (Warning: simple math ahead so non-math types bear with me).

## Key Points

• Simple interest is an interest rate applied only to a principal of a loan
• Compound interest is an interest rate applied to the principal and accrued interest on a loan
• Nominal interest rates are the quoted rates
• Real interest rates are quoted rates adjusted for the effects of inflation

## Simple vs. Compound Interest

Let’s start with an example. Say you go to Richguy Bank in Rainbowville and take out a \$1,000 loan and plan to pay off the loan in 3 years. The banker tells you that each year you are charged 5% on the loan. You still need to know does this interest compound or is it a simple interest rate. What’s the difference? A lot of money you could owe.

To start let’s define the \$1,000 as our principal. The principal amount is just the amount we have borrowed. Now we also have the interest rate of 5% (in this case I defined as yearly where most interest rates are monthly) and a loan term of three years. Now that we have the variables defined let’s finally discuss the difference between the two types of interest. If the interest rate is a simple interest rate (unlikely, most interest rates on borrowed loans are compounded and you will soon see why) the formula to figure out how much money in interest you will owe at the end of the loan is very simple.

## Simple Interest Example

Simple interest owed = Principal * Interest Rate * Term of the Loan

Or to use our numbers:

\$150 = \$1,000 * 0.05 * 3 years

Note: It is important that the rate and the term of the loan are in the same units (i.e. if your interest rate is monthly the term of the loan would have to be in months)

Alright so that wasn’t too bad. Here’s the issue: most loans are made with a compounding interest rate. This means that the interest rate gets applied to not only the principal, but on the interest that the loan is charged over the time period as well. Let’s use our same example.

## Compound Interest Example

Assuming the same numbers, but now assuming compounding interest
Year 1 : \$50 = \$1,000 * 0.05 * 1 year
Year 2: \$52.50 = \$1,050 *0.05 * 1 year
Year 3: \$55.125 =1102.5 *0.05 * 1 year

Total Interest Owed = Year 1 Interest + Year 2 Interest + Year 3 Interest
\$157.625 = \$50 + \$52.50 + \$55.125

So if you compare the two total interest charges between simple and compound you will see a \$7.625 difference over the three years. You may think that isn’t that much of a difference and I agree. Bear in mind though that this is a very simplified example. In most cases the compounding is not done yearly, but monthly. That is the interest owed is calculated based on the principal and added interest on a monthly basis. When I discuss credit card interest rates you will fully appreciate the difference this makes. For now just remember that compounding interest charges you “interest on interest” that is your interest rate is based on principal and added interest while simple interest is only based on principal.

## Nominal vs. Real Interest Rates

#### Nominal Interest Rates

So let’s say you finally invest and go online and check your portfolio and your portfolio website says you earned a 5% return. That’s great right? Well….yes and no. Yes it is good that the return is positive and not negative, but that 5% return may not actually be a 5% return. How is that? Simple….thank inflation. Inflation can be best thought of as a general increase in prices over time (Think of your grandparents and those “Back in my day a gallon of milk cost \$0.05 stories). Inflation eats away at your returns as it raises the price of goods thus lowering your buying power. I will explain more in my inflation lesson but for now remember inflation = bad for your return.

So what does inflation have to do with nominal returns? The 5% return you earned is called the nominal return as it does not account for inflation. Basically any quoted returns in the market place or on securities is a nominally quoted return. Nominal returns are so widely accepted as the standard that when someone refers to their “10% return” rest assured that he/she is quoting a nominal rate. However the nominal rate is less important than the real rate.

#### Nominal Interest Rate Example

Say your portfolio earned 100% return over 10 years. Woah look at you! Your portfolio worth doubled! Unfortunately during that time inflation increased 99% meaning that the cost of all goods and services (gasoline, cheeseburgers, lubricants, haircuts) nearly doubled as well. You may have near double the worth but the cost of the things you would use that worth on have nearly doubled as well. Thus you are not that much better off. Some of you may see that you are only 1% (100%-99%) better off. This is known as the real rate of return.

#### Real Interest Rate

The real interest rate is more important than the nominal rate as it truly reflects the increase or decrease in the worth of your investments.
To calculate real interest rate:

Real Interest Rate = Nominal Interest Rate – Inflation
1% = 100% – 99%

Let’s use another example. Say that your portfolio earned 5% return and over the time period inflation was 10%.

-5% = 5% – 10%

As you can see your real return in this case was actually negative though it seems your return was positive. You may be thinking “If real interest rates are more important why don’t people use it?” The answer to that is inflation is a very tricky thing to measure and even harder to put an exact number on it. So just remember that inflation does play a role in measuring your returns.

## Definitions

1. Simple Interest: interest applied only to the principal of a loan
2. Compound Interest: interest accrued from principal and added interest of a loan
3. Principal: the borrowed amount of a loan
4. Loan Term: the time period of the loan
5. Nominal Interest rate: quoted interest rate
6. Real Interest rate: a quoted interest rate adjusted for inflation
7. Inflation: a general increase in prices over time that decreases buying power