All Terrain Thinking

A Compendium of things I think are Important

Economics: It's not just whats' in your wallet

Interest rates: A closer look at inflation

Inflation effect: lenders want higher rates if prices are rising faster

A Simple Example

To see the impact of inflation on interest rates, let's look at a simple example. Assume you borrow $100 today and promise to pay back $105 one year from today. The lender will have been paid $50 for the use of that money for a year and the lender will use the $105 next year to buy a new pair of sneakers.

It sounds like a mutually beneficial trade, but what happens if the price level changes? The mathematics of the example have been worked out below.

When 5% is not 5%

Nominal rate	5.0%	5.0%	10.0%
Inflation rate	0.0%	5.0%	5.0%
Real rate	5.0%	0.0%	5.0%
Loan	$100	$100	$100
Interest paid	$5	$5	$10
Total payment	$105	$105	$110
Cost of living	$100	$105	$105
Gain to lender	5%	0%	5%

Column 1: you pay 5% interest in zero inflation world. When you repay $105 in one year, the lender can buy $105 worth of 'stuff'. The lender's buying power has been increased by 5% by waiting a year. The real rate of return is 5%.

Column 2: you pay 5% interest in 5% inflation world. When you repay $105 in one year, the lender can buy $105 worth of 'stuff', but the cost of living has risen 5%. This means it now costs $105 just to stay even, to buy what we used to buy with $100. The lender's buying power has not been increased by waiting a year. The real rate of return is 0%.

Column 3: you pay 10% interest in 5% inflation world. When you repay $110 in one year, the lender can buy $110 worth of 'stuff', but the cost of living has risen 5%. This means that the lender now has $110 and costs are $105 just to stay even. In this case the lender's buying power has not been increased by 5 % as a result of waiting a year ($110/$105 = 5%). The real rate of return is 5%.

Real and Nominal Interest Rates: The Math

Are there any generalizations we can make from our simple example? If we ignore all of the other components/dimensions of the interest rate, we can specify the relationship between real and nominal interest rates as follows:

r_n = r_r + i_e

or

r_r = r_n - i_e

• r_r = real rate
• r_n = nominal rate
• i_e = expected inflation rate

Real and Nominal Interest Rates: The Track Record

Short-term Government Rates

	Nominal	Inflation	Real
1950-59	2.03	2.25	-0.22
1960-69	4.00	2.53	1.47
1970-79	6.32	7.41	-1.09
1980-89	8.85	5.12	3.73
1990-95	4.87	3.33	1.53

The track record: a graph

Inflation and Nominal Interest Rates

Nominal Rates

Real Interest Rates

 

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