Difficulty: Introductory | Prerequisites: Basic arithmetic, understanding of percentages. Familiarity with money supply measures (M0, M1, M2) is helpful but not required.
Interest rates are the price of borrowing money, and they sit at the centre of macroeconomic policy. The Federal Reserve raises or lowers interest rates to influence spending, saving, and investment across the entire economy. But "the interest rate" is not one number: there is a critical difference between the nominal rate (what the bank quotes you) and the real rate (what your money actually earns after inflation eats into it). This topic also covers the inverse relationship between interest rates and bond prices, a relationship that trips up students regularly but is straightforward once the logic clicks. You need this material before studying the Fed's tools, the loanable funds market, or anything involving the bond market.
The nominal interest rate is the stated rate. The real interest rate is the nominal rate minus expected inflation, and it tells you how much purchasing power you actually gain. When interest rates fall, existing bond prices rise (and vice versa), because older bonds with higher fixed payouts become more valuable relative to new, lower-paying ones.
Nominal Interest Rate
The stated or advertised interest rate on a loan, bond, or deposit. It does not account for inflation. In simple terms, it is the number the bank puts on the sign.
Real Interest Rate
The nominal interest rate adjusted for inflation. It measures the actual increase in purchasing power. Think of it as what your money really earns after prices have risen.
Expected Inflation Rate
The rate at which prices are anticipated to rise over a given period. It is a forecast, not a known quantity, so the "expected real interest rate" is also an estimate.
Fisher Equation (Approximate)
The formula linking nominal rates, real rates, and inflation: real interest rate ≈ nominal interest rate − expected inflation rate. This approximation works well when rates are low (under about 10%).
Government Bond
A debt instrument issued by a government. The bondholder lends money to the government in exchange for periodic interest payments (coupons) and the return of principal at maturity. Bond prices move inversely to prevailing interest rates.
Inverse Relationship (Interest Rates and Bond Prices)
When market interest rates go down, existing bond prices go up, and when market interest rates go up, existing bond prices go down. This is a mechanical relationship, not a theory.
The Fisher equation (approximate form): Real interest rate ≈ Nominal interest rate − Expected inflation rate
This tells you how much purchasing power you gain, after accounting for rising prices.
Worked example from the source material:
A bank offers a 5-year CD at 3% nominal interest. Expected inflation is 1%.
Real interest rate ≈ 3% − 1% = 2%
The CD earns you 3% in dollar terms, but prices are expected to rise by 1%, so your real gain in purchasing power is about 2%.
If expected inflation were higher than the nominal rate (say, 4%), the real interest rate would be negative (3% − 4% = −1%). You would be losing purchasing power even while earning interest.
The exact Fisher equation is (1 + r) = (1 + i) / (1 + π), where r is the real rate, i is the nominal rate, and π is the inflation rate. The approximate version (r ≈ i − π) is what you will use on exams unless told otherwise.
This is one of the most frequently tested relationships in introductory macro. Here is the intuition:
A bond pays a fixed amount (its coupon) each year. Say a government bond pays $50 per year.
If prevailing interest rates in the market are 5%, a new bond that costs $1,000 would also pay $50 per year. So the existing bond is priced at roughly $1,000, because it offers the same deal.
Now suppose market interest rates fall to 4%. A new $1,000 bond would only pay $40 per year. The existing bond still pays $50, making it more attractive. Buyers will bid its price up until the $50 coupon represents a 4% return on the purchase price. That happens at $50 / 0.04 = $1,250.
The existing bond's price rose from $1,000 to $1,250 because interest rates fell.
The reverse works the same way: if market rates rise, new bonds offer better payouts, making existing bonds less attractive, so their prices fall.
Applied to the source question:
Banks across the country are decreasing nominal interest rates. What happens to government bond prices?
Government bond prices will increase. Lower market interest rates make existing bonds (with their higher fixed coupon payments) more valuable by comparison.
Central bank policy changes interest rates.
Bond prices adjust as a consequence.
Students sometimes get confused about which causes which. In practice, bond prices and interest rates are determined simultaneously in the market, but for introductory macro: think of interest rate changes as the cause and bond price changes as the effect.
Fisher Equation (Approximate):
Real interest rate ≈ Nominal interest rate − Expected inflation rate
r ≈ i − π
Fisher Equation (Exact):
(1 + r) = (1 + i) / (1 + π)
Bond Price Approximation (for a perpetuity / consol):
Bond price ≈ Annual coupon payment / Market interest rate
This simplified formula shows the inverse relationship directly: as the denominator (interest rate) falls, the price rises.
When you hear news reports that "the Fed cut rates and bond markets rallied," this is the inverse relationship in action. Existing bondholders see the value of their holdings increase whenever rates fall. Pension funds, insurance companies, and anyone holding government bonds cares deeply about interest rate movements for exactly this reason.
The real interest rate matters for everyday decisions too. If your savings account pays 4% but inflation is 3.5%, you are barely growing your purchasing power. Understanding the distinction between nominal and real rates prevents you from being misled by headline numbers.
"A higher interest rate is always better for savers." Not necessarily. If inflation rises faster than the nominal rate, the real return falls. A 5% nominal rate with 6% inflation leaves you worse off in real terms.
"Bond prices and interest rates move in the same direction." They move in opposite directions. This is the single most common error on this topic.
"When interest rates fall, bonds become a bad investment." The opposite is true for existing bondholders: their bonds increase in value. Falling rates are bad for people buying new bonds (lower yields), but good for those who already hold bonds.
"The real interest rate is always positive." It can be negative when inflation exceeds the nominal rate. This has happened in several recent periods in major economies.
⚠️ You will almost certainly be asked to calculate a real interest rate using the Fisher equation. Know the formula cold.
⚠️ The inverse relationship between interest rates and bond prices is a staple exam question. Be prepared to explain the mechanism, not just state the direction.
⚠️ Pay attention to whether a question asks about the effect on new bonds vs. existing bonds. Falling rates make existing bonds more valuable but give new bonds lower yields.
⚠️ Distinguish between the nominal rate and the real rate. If a question mentions inflation, it is asking about the real rate.
True or False: If the nominal interest rate is 6% and expected inflation is 2%, the real interest rate is 4%. True.
True or False: When nominal interest rates decrease, government bond prices decrease. False. Bond prices increase when interest rates decrease.
Fill in the blank: Real interest rate ≈ ______ − expected inflation rate. Nominal interest rate.
True or False: A negative real interest rate means the bank is charging you to hold your money. Not exactly. It means inflation is eroding your purchasing power faster than the nominal interest payment is adding to it. Your balance still grows in nominal terms, but buys less.
Q: A bank offers a 5-year CD at 3% interest. Expected inflation is 1%. What is the expected real interest rate? Show your work.
A: Real interest rate ≈ Nominal rate − Expected inflation = 3% − 1% = 2%.
Q: Banks across the country are decreasing nominal interest rates. What happens to government bond prices?
A: Government bond prices increase. Existing bonds with higher fixed coupon payments become relatively more attractive when new bonds offer lower rates, driving up the price of existing bonds.
Q: If the nominal interest rate is 2% and expected inflation is 3%, what is the real interest rate, and what does it imply?
A: Real interest rate ≈ 2% − 3% = −1%. A negative real rate means the saver is losing purchasing power despite earning nominal interest. The money in the account grows, but prices are rising faster.
Q: Explain why the inverse relationship between interest rates and bond prices exists.
A: Bonds pay a fixed coupon. When market interest rates fall, newly issued bonds pay less than existing ones. Investors are willing to pay more for the existing, higher-paying bonds, pushing their prices up. The reverse holds when rates rise: existing bonds look less attractive, so their prices fall.
This material links directly to monetary policy (how the Fed uses interest rate targets to influence the economy), the loanable funds market (where the real interest rate is the price that equilibrates saving and investment), and aggregate demand (interest rates affect consumption and investment spending). It also connects to the money supply topic: when the Fed adjusts the money supply, interest rates change, which in turn moves bond prices. Understanding these connections is essential for exam questions that span multiple chapters.
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