BYMIKE FLADLIEN

MUSCATINE HIGH SCHOOL

Real Interest Rate

What is the “nominal interest rate”?

The nominal interest rate is the interest rate expressed as a percent. The nominal interest rate is printed on a bond, savings accounting passbook, mortgage, or other financial instrument. For example, Juan may have a loan at Hill’s National Bank that is charging 8% interest. Won may have a savings bond that pays 10%. Greg Mankiw defines the nominal interest rate “as the rate the bank pays.” The nominal interest rate is not the purchasing power. Sometimes the interest rate is described as the cost of using money.

Question 1

Answer this question as “true” or “false”.

T F Greg is thinking about buying a new car. The sticker posts an APR of 1.9% interest. The 1.9% is the nominal interest rate.

If Maggie borrows $100 for 1 year at 10% interest rate, how much is the

nominal interest rate?

The nominal interest rate is 10%. Fill in the blank with the correct word or words to complete the sentence.

Question 2

William wants a student loan to attend Buffoon University. First National Bank of Buffoonia will loan William tuition at 6% per year. The nominal interest rate is ______.

How much will Maggie have to pay back in dollars if she borrows $100 for 1 year at 10%?

Maggie will have to pay back $10. (Multiply the principal, $100, rate of interest in percent, 10%, and the time in years, 1, and you will arrive at $10. That is, $100(.10)(1) = $10. To generalize the concept, 1 + i represents the nominal interest rate. So I could have multiplied $100(1.10) to see that the total amount Maggie would have to pay back is $110. Subtracting $100 from $110 would be $10.

Question 3

Calculate the amount of nominal interest for Won I Chang. Won loans Christie $500 at 12% for 1 year. How much interest in dollars will Won receive when the loan is due? ______.

$10. I multiplied the principal times the rate times the time. That is, $100(.10)(1). Since multiplication is commutative, the order does not matter.

Suppose that Juan loaned the $100 at 10% for one year to Maggie. How much will Juan receive from Maggie on the due date in nominal terms?

Question 4

Suppose that Juan loaned the $100 to Maggie at 15% for the year. How much would Maggie pay on the due date? ____

Suppose that Juan loaned the $100 to Maggie at 15% for the year. How much would Maggie pay on the

due date? ____

The real interest rate is the buying power of the interest in dollars. The real interest rate is the amount of purchasing power after interest is paid or collected after adjusting for inflation.

To find the purchasing power of the amount of nominal interest collected or paid, simply divide the amount of interest in dollars, by the price level. On the next slide, let’s look at how the price level affects the purchasing power of $100. The $100 could have been saved or loaned.

How do I calculate the “buying power” after a loan has been paid

or collected?

Purchasing Power at Three Price Levels

Principal Price Level (Price Deflator)

Purchasing Power

$100 100 $100$100 200 $50$100 50 $200

The price level changes the purchasing power of $100. If the price level is high such as at 200, the $100 only buys $50 in real goods. If the price level is low such as at 50, $100 buys $200 dollars of real goods.

When the price level was high, 2, the interest collected lost buying power. This is good for the debtor but bad for the creditor. When the price level was low, the purchasing power of the interest collect increased. This is bad for the debtor and good for the creditor. So when people say that inflation is “bad” they are not seeing the whole picture. Inflation as reflected in the price level distorts the purchasing power of the interest collected and redistributes wealth in ways unintended.

Why did the purchasing power change as the price level changed?

What is a change in the price level called?

A change in the price level can either be called inflation or deflation. A positive change in the price level is inflation. Such a change might be a change from 1.04 to 1.06. A negative change in the price level is deflation. Such a change might be a change from 1.06 to 1.02.

Question 5

There are two price levels used in AP Macro. What is the price level called that uses a fixed market basket? _____________ The other price level divides nominal GDP by real GDP. This price level is called ____________________. If an economist wanted to see how much production was growing, which price level would she use?

Now let’s generalize the concepts so we can move on to application.

Let 1 + i be the nominal interest rateLet 1 + π be the inflation rateLet 1 + r be the real interest rate

When I write “generalize” I mean that I’m to construct the real interest rate formula that economists use to find the real interest rate

What is the equation I use to find the real interest rate?

r is the real interest rate; i is the nominal interest rate; and π is the inflation rate.

Using the formula from step 10 and subtracting 1, the answers are .10, .048, and .16.

How much does the real interest rate equal in each of the following cases? 1.10/1? 1.1/1.05? 1.1/.95?

How can I approximate those values?

You can get approximately the same values by simply subtracting the numerator and the denominator. For example, 1.10 – 1 = .10. 1.10 – 1.05 = .05. and finally, 1.10 - .95 = 15.

What is the Fisher Equation?

The Fisher Equation which is: r = i - πwhere r is the real interest rate, i is the nominal

interest rate, and π is the inflation rate. The Fisher Equation approximates the nominal interest rate. In step 12, I found the real interest rate. I subtracted the inflation rate from the nominal interest rate. In step 13, I rearranged the equation into the Fisher Equation. The Fisher Equation states that the nominal interest rate equals the real interest rate minus the inflation rate for small changes in the inflation rate.

What is the real interest rate?

The real interest rate is the amount of interest the creditor receives or the debtor pays after subtracting inflation.

Why is the real interest rate important?

The real interest rate is important because inflation may catch lenders off guard. These lenders will receive less interest in terms of buying power than they would have if they fully anticipated inflation. Inflation can help the debtor when inflation isn’t fully anticipated. The debtor is helped because the debtor repays the interest will dollars that don’t buy as much as when the dollars were loaned. The real interest rate is important when performing cost-benefit analysis, indexing bonds to the Consumer Price Index, or making monetary policy.

Question 6

Nominal Interest Rate

Inflation Rate Real Interest Rate

10% 8%6% 6%12% 10%3% 1%2% -4%

Complete the table for Question 6 by finding the real interest rate.

The End

For questions or comments, write to me at

mfladlien@gmail.com