## Calculating interest rates on a yearly basis, Macroeconomics

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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.

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