 # Interest rate

## Introduction

When you borrow money, you usually have to pay a fee for the loan. This fee is often called interest, particularly if the fee is proportional to the amount you borrow. The interest rate is commonly expressed as a percentage of the size of the loan per unit of time, typically per year. If the interest rate is 10% per year, you must, for example, pay 1,000 per year if you borrow 10,000.

The interest rate may be fixed or floating. If it is fixed, you will pay the same percentage for the entire duration of the loan. With a floating interest rate, the interest rate will change regularly depending on market conditions.

The Interest rate for a specific loan depends on the general level of interest rates as well as the specifics of the loan. Factors such as risk (the probability that the loan will not be repaid), duration of the loan and whether you select a fixed or a floating rate will influence the interest rate.

## Market interest rates

The most important interest rates from a macroeconomic perspective are interest rates that the government pays on the loans they use to finance the national debt. The government borrows money by issuing government bonds. All such bonds have a fixed nominal amount and a given maturity date. The government promises to pay exactly the nominal amount (also called the principal or the face amount) to the holder at the maturity date. Some bonds also promise regular payments, so-called coupon payments, at regular intervals, the coupon dates.

In most countries you will find many types of government bonds. An important distinction is the duration of the bond, that is, the difference between the maturity date and the date when the bond was issued. For example, in the United States, government bonds maturing in one year or less are called Treasury bills.

Typically, bonds with a maturity of a year or shorter have no coupons. Instead, they are sold below the nominal amount at what is called the issue price. The issue price for a bond without coupons must be below the nominal amount. For example, if you pay 23,500 for a bond with a nominal amount of 25,000 maturing in one year, your interest rate is (25 000 - 23 500)/23 500 = 6.38%.

In most countries, you also find government bonds with longer maturity. For example, in the United States you have Treasury notes (two to ten years) and Treasury bonds (10 years or longer). Government bonds with longer maturity typically make coupon payments. You will also find other types of bonds

### Relationship between the interest rate and the bond price

Note that the higher the issue price, the lower the interest rate. In the same way, when the price of a government bond increases, the interest rate falls and vice versa. The price of a government bond is normally determined by supply and demand which means that you can understand movements in these interest rates by analyzing the market. For example, if the government needs to borrow more money, supply increases, bond prices fall and interest rates increase.

### Calculating interest rates on a yearly basis

If the maturity is different from one year, the interest rate is usually recalculated to a corresponding one year rate. For example, consider a bond which matures in six months, has a nominal amount of 25,000 and a current price of 24,200 (no coupons). The six month interest rate is then 800/24,200 = 3.3%. If we want to express this rate as a yearly rate we imagine that we make this investment twice. Our return would then be 1.033-1.033 = 1.067 or 6.7%. Note that if the interest rate is fairly low, then the yearly interest rate is approximately two times the six month interest rate. In the same way, the monthly interest rate is approximately one twelfth of the yearly interest rate.

Keep in mind that the six month interest rate, recalculated to a yearly rate, will typically not be equal to the one year interest rate. For example, suppose that we expect interest rates to increase. In such a case, the yearly interest rate would be an average of the current six month rate and the six month rate six months from now, which is expected to be higher. Hence, the one year rate would be higher than the current six month rate. In the same way, if we expect interest rates to fall, then shorter interest rates will be higher than longer interest rates.

This means that we have many different market rates in a country - rates depending on maturity. Even though rates with different maturity (all recalculated to a yearly rate) need not be exactly equal, they cannot be too different either. This is particularly true for rates with similar maturity. The seven month rate cannot deviate far from the six month rate since they are fairly close substitutes.

### The yield curve

The yield curve is a graph of interest rates of different maturity (recalculated to yearly rates) at a particular point in time. It is common for the yield curve to slope upwards (interest rates with longer maturity are generally higher than those with a shorter maturity). The reason for this is that there is a higher demand for loans with longer maturity due to the reduced uncertainty. Many borrowers are prepared to pay a premium to avoid fluctuations in the interest rates.

As discussed above, if the market expects higher interest rates, then the slope of the yield curve will increase. Although not very common, the slope may be negative if the market expects the interest rates to fall more than the premium on longer rates.

### Other interest rates

There are many other interest rates in a society. For example, you will earn interest when you deposit money in a bank account and you will pay interest when you borrow money. These interest rates will depend on the specifics of the deposit and the perceived risk when you borrow money. However, all interest rates are correlated with the market interest rates. When you borrow money, you typically pay a higher interest rate compared to government bonds, and when you lend money, you will receive a lower rate.