Calculating interest rates on a yearly basis

If maturity is different from one year, interest rate is generally recalculated to a corresponding one year rate. For instance consider a bond which matures in six months, has a nominal amount of 25,000 and a current price of 24,200 (no coupons). Six month interest rate is then 800/24,200 = 3.3%. If we want to express this rate as an annual rate we imagine that we make this investment twice.

Our return would be then 1.033. 1.033 = 1.067 or 6.7%. Note that if interest rate is fairly low, then yearly interest rate is approximately two times the six month interest rate. Similarly the monthly interest rate is approximately one twelfth of the yearly interest rate.

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

This means that we have many different market rates in a country - rates depending on maturity. Although rates with different maturity (all recalculated to a yearly rate) required not to be exactly equal, they can't be too different either. This is certainly true for rates with similar maturity. Seven month rate can't deviate far from the six month rate because they are fairly close substitutes.