Inflation measures the dynamics of the purchasing power of money. In this part of the segment, we address the interaction between inflation and interest rates, that measures the ability of individuals to exchange purchasing power across time through lending markets. We know that the central bank implements monetary policy through adjustment of interest rates. It is important to examine the relationship between inflation and interest rates. Saving and interest as a way of directly growing your purchasing power over time. If you lend money are deposited at the bank, your pot of money can grow at the rate of interest. Inflation measures how quickly the prices rise, but it also represents how quickly the purchasing power of any amount of money will dissipate. If you hide some currency under your bed at the beginning of the year, your spending power at the end of the year will depend on how quickly the prices of things that you want to buy will be increasing. The prices are higher than you hoped, your spending power will be smaller than you thought. We compare inflation with interest rates to examine the rate at which your purchasing power will grow when you save. Consider the interest on a simple time deposit, the depositor puts the principal into the bank at the beginning of the year and the balance of the deposit grows by the interest rate over the year. By definition, the interest rate is the money gained at the end of the year per dollar deposited at the beginning of the year. Also by definition, we can write inflation in terms of the growth in the cost of living, or the gross growth rate of the CPI. Though the growth in the monetary value of the deposit is given by the interest rate, inflation will also determine the growth of purchasing power. The purchasing power of the principal is a principal divided by the CPI, this is a quantity of consumer goods that could be purchased with the amount of the deposit. Likewise, the final balance can be used to purchase goods at the prevailing price next year. The growth rate of purchasing power as a purchasing power at the end of the year relative to the purchasing power of the beginning of the year. Define this return as the real interest rate, one plus small R. With a little algebra, we can rearrange to simplify the formula for the real interest rate. Remember, inflation over the life of the deposit is given as a growth rate of the CPI, and the nominal interest rate is a growth rate at the bank deposit. So the real interest rate is the gross interest rate divided by the gross inflation rate over the life of the deposit. The real interest rate is a nominal interest rate divided by the inflation rate. In other words, the money interest rate can be expressed as a product of two parts, the real interest rate and future inflation. Multiply the right-hand side of the equation through, subtract one from both sides, write the interest rate in net terms. The net nominal interest rate is the real interest rate plus future inflation plus the product of the two. The product of the net inflation rate and the real interest rate is a fraction of a fraction. So for illustrative purposes, we often think of this as approximately zero. This means that we can think of the net interest rate as approximately equal to the sum of the real rate and future inflation, or the real rate is the difference between the interest rate and the inflation rate over the future. Savers try to preserve the purchasing power of their wealth. Preserving this purchasing power is a race between the interest rate on the one hand and the inflation that is occurring on the other. The real interest rate is the lead that the interest rate has over inflation. Consider data from the Philippines, in March 2016, the average interest rate on one year time deposits was 1.61 percent. However, over the year between March 2016 and March 2017, the CPI increases from 142.6 to 147.5. As we saw just a few minutes ago, this is equivalent to inflation of about 3.44 percent. Calculate the real interest rate in March 2016. Consider the purchasing power of someone who deposited peso into a time deposit in the Philippines, in March 2016. The real interest rate represents the growth of their purchasing power. We can calculate this as gross interest divided by gross inflation. The growth of their bank balance will be the interest rate which is 1.61 percent. However, the purchasing power of any peso is declining as the cost of living grows with the CPI. The gross real interest rate is 1.0161 divided by the gross inflation 1.034, this equals 0.9823. The net real interest rate r can be calculated as about negative 0.18 or negative 1.8 percent. A negative real interest rate means that inflation is so high relative to the money interest rate, that a saver will actually be losing purchasing power when they save. Alternatively, we can use a simple approximation, the nominal interest rate is 1.6 percent and the inflation rate is 3.4 percent. So, the real interest rate is 1.6 percent less expected inflation which is equal to negative 1.8 percent. Real interest rates are the difference between the interest rate and inflation over the course of time. Consider also the real interest rate from the perspective of a borrower, considering taking out a loan. With 2020 hindsight, we will be able to know what the real cost of borrowing was after the money was repaid, which we call the ex post real interest rate. This is simply the money interest rate less actual observed inflation. The real interest rate can also be viewed from the ex ante standpoint of the time at which the loan was made. At that time, neither the lender nor the borrower will know what inflation will occur over the life of the loan. We define the ex ante real interest rate as a difference between the money interest rate and the best forecast of future inflation. The ex ante real interest rate is important because borrowers make their decision based on this real interest rate. Since borrowers usually spend the funds borrowed, there is a connection between the real interest rate and different categories of spending. When interest rates are high, there'll be less spending especially on items like housing and automobiles, and other consumer durables. Consider some data from Japan on the one year Tokyo interbank offered rate interest rate. For example, in January 2016, this was 0.29 percent. The Japan Center for Economic Research publishes its ESP forecast survey for the CPI inflation over the next year. At the beginning of 2016, forecasters expected inflation over the subsequent year to be 0.99 percent. We could use this expected inflation to calculate the ex ante real interest rate, as the difference between the interest rate and the expected inflation rate. The ex ante real interest rate can be used as an indicator for the relevant costs of borrowing in the economy. After completing this segment, you should have learned to one, calculate the annualized inflation rate, two, calculate the real interest rate. As we wrap up, let's conclude by summarizing the key question. How do we define and measure price stability? Money is valued because it provides purchasing power. The Consumer Price Index is a tool that allows us to measure purchasing power of money that is held by consumers. Inflation is the growth rate of the CPI, thus, price stability can be measured as a low and stable growth rate of this price index. Now, the Central Bank sets interest rates measured in money. Adjusting interest rates for inflation allows us to measure the real return to saving and purchasing power terms. The real expected interest rate is calculated on an ex ante basis at the beginning of a lending arrangement based on the known nominal interest rate in a forecasts of future inflation. The real interest rate can also be calculated on an ex post basis at the end of a loan. Stable inflation will thus make the ex post real interest rate more predictable. Now, let's move on to think about the benefits of price stability in the next segment.