# The Relationship Between Interest Rate & Inflation

The nominal rate of interest is the stated rate that contracts are based on. It is approximately equal to the real rate of interest plus the inflation rate. From the perspective of investing or loaning money, lower inflation rates are desirable because they imply higher real rates of interest. From the perspective of a borrower, lower inflation rates can increase the real value of outstanding debt.

## Interest rates, Inflation and Lending

You have $10,000 today that you want to save in order to pay for tuition next year. The tuition costs $10,000 today, but may be higher next year due to inflation. You consider buying a one-year bond offering a yield of 4 percent so that you'll have $10,000 (1 .04) = $10,400 when it's time to pay for tuition. If inflation turns out to be 3 percent, the tuition bill is $10,300, and you have an extra $100. The nominal interest rate was 4 percent, but the real interest rate is approximately 1 percent. If the inflation rate turns out to be greater than 4 percent, the real rate of interest will be negative and you won't have enough for tuition.

## Exact Relation

The exact real rate can be found by dividing the purchasing power of the money repaid by the purchasing power of the money lent. The $10,400 to be paid back to you is worth only $10,400 / (1 + 3 percent inflation) relative to the beginning of the period, or $10,097.09. Therefore the real rate of interest is $10,097.09 / $10,000.00 - 1 = 0.97 percent. The exact equation relating nominal rates, real rates and inflation rates is (1 + real rate) (1 + inflation rate) = (1 + nominal rate). This is approximately the same as nominal rate = real rate + inflation rate, because the term from multiplying the real rate and inflation rate is very small and can often be ignored.

## Interest rates, Inflation and Borrowing

Instead suppose you don’t have money for tuition and you borrow $10,000 today. You agree to pay it back next year at a stated, nominal rate of 5 percent. If the inflation rate turns out to be 6 percent, the real rate of interest that you must pay is negative, approximately -1 percent -- and you're better off, economically, than before you took the loan. You must pay back $10,500, but it's worth only $10,500 / (1 + 6 percent) = $9,905.66 compared to when you borrowed the $10,000. Usually of course, the inflation rate is less than the nominal rate and the real rate of interest is positive.

## Negative inflation

On the other hand, if inflation is low, or negative, the value of the debt that you owe increases. For example, if there is deflation, so that the inflation rate is -1 percent, the amount that you must pay back on a 5 percent $10,000 loan is worth (in terms of the beginning of the year), $10,500 / (1 – 1 percent) = $10,606.06. The impact of deflation is positive then for investors or lenders: The amount they receive is worth more than that implied by the nominal rate.

References

- Investments: Bodie, Kane and Marcus

Writer Bio

Kathryn Christopher has been writing about investments for more than 20 years. Her work has appeared in the "Journal of Alternative Investments" and numerous other academic and industry publications. She works at Wiggin Financial Planning, teaches for UMASSOnline from South Florida, and holds a PhD in finance from the University of Massachusetts.