Inflation focuses on the value of domestic money. It starts by measuring the amount of currency it takes to buy a small bit of GDP — for example, $0.10 to buy a candy bar in 1963 or $1 in 2016. Thus, the fundamental variable is the rate of exchange between money and goods and services at a single point in time.
By contrast, the interest rate is a different kind of price because it looks at rates of exchange between different points in time. A bank offering an annual interest rate of 5 percent, for example, is promising to trade a deposit of $1,000 dollars today for a payoff of $1,050 one year from now. The trade is explicitly between dollars today and dollars in the future. The price is that $1 today "buys" $1.05 dollars in one year. That intertemporal price is what the 5 percent interest rate measures.
Notice that in that example, the trade is between dollars now and dollars later. Economists call this the nominal interest as opposed to the real interest rate. This is because unless you have a strange definition of a "green" diet, what the money is really good for is buying stuff — food (candy bars included), housing, transportation, and so forth. It's these things that you really care about.
So, returning to the story, suppose you deposit $1,000 in the bank today and then withdraw the promised principal plus 5 percent interest of $1,050 in one year. Meanwhile, inflation over that year runs at 5 percent. That means that when you get the payoff of $1,050 it takes that much just to buy the same goods you bought with $1,000 a year earlier. In terms of the goods that really matter to your well-being, you haven't gained a thing. That is, what economists call the "real" interest rate is, in this case, zero. Just remember the simple formula:
Real rate = Nominal rate – Inflation rate
The (real) interest rate is an important variable in macroeconomics. It can have a big impact on the behavior of consumers and firms:- Individuals: Imagine that the interest rate is very high, so you get a large return on your savings. How would that affect your choices? Well, probably you'd think twice before spending your money. After all, if you spend it now, you give up the opportunity to save it and earn a high return. In this situation, economists say that the opportunity cost of consuming is high. Similarly, if you want to buy a car or a house and you need to borrow money, you're much less likely to do so if the real interest rate is high.
- Firms: Large firms, especially, often have surplus cash lying around. What should they do with it? One option is to save it and earn the interest rate. Another option is to buy some more capital. If the interest rate is high, buying a new machine had better give the firm a really good return — otherwise it should have just saved the cash and earned the interest rate return.
If the interest rate is high, not many firms want to invest in new capital. Conversely, a low interest rate makes capital investment very attractive.
You need to be clear about how economists understand those two words, investment and capital. They may well be the most easily misunderstood terms that economists use (not counting efficiency, economic profit, elasticity, and about 100 others). What an economist and non-economist mean by them is very different.