Every interest rate you see is quoting two things at once: what the money costs to rent, and what the lender expects the money to be worth when it comes back. Mix them up and a lot of financial news stops making sense. Why does a bond lose value when "rates rise"? Why can a savings account paying 2% leave you poorer? Why does a fixed-rate borrower sometimes win?
This module separates the two parts. You will see inflation in three economies, split a 10-year interest rate into its real part and its inflation part, then play with two simulators: one for the price of a bond, one for what inflation does to savings and to debt.
Inflation is the rate at which prices rise. Statistics offices measure it by pricing a fixed basket of things households buy (food, rent, fuel, clothes, phone plans) every month and comparing the basket's cost with the same month a year earlier. The result is a consumer price index. If it says 3%, the basket costs 3% more than it did twelve months ago.
Three things people miss. First, it's a rate. When inflation falls from 9% to 3%, prices don't fall back. They keep rising, just more slowly, and the higher price level stays. Second, it's an average basket, not yours. If you rent and drive a lot, or own your home and walk to work, your own inflation differs. Third, it doesn't track the price of assets. Consumer indexes count the cost of living in a home (rent, or what owners would pay as rent), not what houses or shares sell for. The three series below also use different baskets and methods, so compare their direction and size, not the second decimal.
Each line is the change in consumer prices from the same month a year earlier. Hover for values. The Czech series ends in April 2025 in the data we pulled, so it stops there on purpose.
US inflation peaked at 8.98% in June 2022 and the euro area at 10.62% in October 2022. In September 2026 they stood at 3.72% and 3.75%. The Czech Republic went from 2.16% in January 2021 to 17.97% in September 2022, then back to 1.85% by April 2025, the last point we have. Its record in this data is 21.90% in April 1993, in the early years of the post-communist transition.
A nominal rate is the number on the contract. A real rate is what's left after inflation: roughly the nominal rate minus inflation. Lend $1,000 at 3% for a year while prices rise 5%, and you get $1,030 back. That buys what $981 bought a year earlier. You earned 3% and lost about 1.9% in real terms.
The catch is that the inflation you'll face is unknown when you lend. So there are two real rates. The one looking back (nominal minus the inflation that actually happened) and the one the market sets looking forward. The US Treasury sells bonds that make the forward one visible: TIPS, whose principal rises with consumer prices. A TIPS yield is a real yield, the return promised above inflation, whatever inflation turns out to be.
Looking back, the 10-year Treasury yielded 1.47% in December 2021 while US prices were rising 7.17% a year. Looking forward, the real yield on 10-year TIPS that month was minus 0.99%, and it hit minus 1.07% in August 2021, the lowest in the data. The lender was paying for the privilege of holding the bond. By September 2026 the 10-year nominal yield was 4.99% and the real yield 2.64%.
Switch between the two views. In the first, the gap between the lines is the inflation lenders are pricing in. The second shows that gap directly, next to what inflation actually did. The breakeven in the second view is computed here as nominal minus real, month by month.
Put the two yields side by side and the gap between them is the breakeven inflation rate. It's the yearly inflation at which an ordinary Treasury and an inflation-protected one end up paying the same. If you expect inflation above it, TIPS look better. Below it, the ordinary bond does. Many people read it as the market's inflation forecast.
It's a rougher tool than that. The gap also holds payment for the risk that inflation surprises, and for the fact that TIPS trade less easily than ordinary bonds. In November 2008 the 5-year breakeven fell to minus 1.4%, which no one believed was a forecast of falling prices. It reflected a market under stress. What the breakeven does show well is the lender's demand: in September 2026 the 10-year breakeven was 2.35%, so a lender buying the 10-year at 4.99% was asking for about 2.35 points to cover expected inflation and 2.64 points on top of it.
The rule of thumb: nominal rate = real rate + expected inflation. That's why rates tend to climb when inflation does. Lenders aren't punishing borrowers. They're refusing to be repaid in money worth less than the money they handed over. The 5-year breakeven went from 1.87% in December 2020 to 3.41% in March 2022 as prices accelerated, the highest in the data. The 10-year yield, which sat at 0.62% on average in July 2020, was 4.80% by October 2023.
A bond is a promise to pay fixed amounts on fixed dates: a coupon every six months and the face value at the end. The yield is the return a buyer earns if they pay today's price and keep it to the end. The price and the yield are the same fact seen from two sides.
Say you bought a 10-year bond at 100 that pays 4% a year. A year later, new bonds pay 5%. Who buys yours at 100, when 5% is available next door? Nobody. To sell, you have to cut the price until a buyer gets 5% on it too. Run the numbers and 100 becomes 92.21. Yields falling to 3% does the reverse: your 4% bond is now worth 108.58.
If you hold it to the end, you still receive every coupon and the full 100. The fall hurts if you must sell before then, or if your fund marks its holdings to market prices, which most do. A hypothetical bond bought at par in July 2020 with a 0.62% coupon (the 10-year average that month), with 7 years left when yields were 4.80% in October 2023, would be priced at 75.40. That's a 25% loss on paper from yields alone.
Duration answers one question: how much does the price move for each 1 point change in yield? A bond with a duration of 8 falls about 8% when yields rise by 1 point. It's measured in years because it's a weighted average of when you get your money back. The longer you wait, and the less you get along the way, the more sensitive the price.
So a 2-year bond with a 4% coupon drops to 98.12 when yields go to 5%. A 30-year bond with the same coupon drops to 84.55. A zero-coupon bond, which pays nothing until the end, has the longest duration for its maturity (a 10-year one goes from 67.30 at a 4% yield to 61.03 at 5%). Try it yourself: drag maturity and coupon and watch the curve steepen.
You bought the bond at 100 when market yields equalled its coupon. Move the market yield and see the new price, the percentage change, and the formula with your numbers in it.
Price = sum over each payment t of cash(t) / (1 + y/2)^t, with t counted in half-years
Here: cash = 2.00 every six months for 20 payments, plus 100 at the end; y = 5.00% so y/2 = 2.500% per half-year.
Result: 92.21. Duration estimate: price change is about -8.18 x (5.00 - 4.00) = -8.18%. The estimate is close for small moves and drifts for big ones, because the real curve bends.
New bonds pay 5.00%, yours pays 4.00%. Nobody pays 100 for the weaker one, so its price falls until a buyer of it also earns 5.00% a year. You get the same coupons and the same 100 at the end, so the buyer pays less today. Hold it to maturity and you still get 100 back. The price change only bites if you sell early or have to mark it down.
Savings are a fixed claim in dollars. If the account pays less than inflation, the balance grows and its purchasing power shrinks. Put $10,000 in an account paying 2% for 10 years while inflation runs at 3% and you end up with $12,190, which buys what $9,070 buys today. Under the mattress it would be worth $7,441. At the US peak rate of 8.98% for a decade, $10,000 of idle cash would be down to $4,232 in today's money. That's the case for looking at the real rate, not the printed one.
Debt is the same arithmetic from the other side. A fixed-rate borrower repays fixed dollars, so rising prices make each dollar easier to earn. That helps borrowers and costs lenders, if the inflation was a surprise. When it's expected, lenders have already put it into the rate, which is why a borrower only comes out ahead when inflation beats what the lender assumed. Variable-rate loans hand the surprise back to the borrower: the rate resets higher. Module 4 comes back to this when the borrower is a government.
Pick an amount, a number of years, an inflation rate and a rate on the savings or the loan. Switch the side to see how the same inflation helps a debtor and hurts a saver.
Dollars after n years = amount x (1 + rate)^n = $10,000 x (1 + 0.020)^10 = $12,190
Today's purchasing power = dollars / (1 + inflation)^n = $12,190 / (1 + 0.030)^10 = $9,070
Your savings grow in dollars and shrink in what they buy: $12,190 in the account is worth $9,070 in today's prices, $930 less than you put in. Cash would have lost more.
A bond pays fixed amounts. When new bonds pay more, an older bond only sells if its price drops until a buyer earns the new yield on it too. A 10-year bond paying 4% falls from 100 to 92.21 if market yields go to 5%, and rises to 108.58 if they fall to 3%.
The rate left after inflation, roughly the nominal rate minus inflation. Lend $1,000 at 3% while prices rise 5%, and the $1,030 you get back buys what $981 bought a year earlier. In September 2026 the 10-year Treasury yielded 4.99% and the 10-year TIPS real yield was 2.64%.
The gap between an ordinary Treasury yield and an inflation-protected (TIPS) yield of the same maturity: the yearly inflation at which both pay the same. The 10-year breakeven was 2.35% in September 2026. It also carries risk and liquidity premiums, so it is a rough read of expectations, not a forecast.
Savings that earn less than inflation lose buying power: $10,000 at 2% for 10 years with 3% inflation grows to $12,190 but buys what $9,070 buys today. Fixed-rate debt gets lighter in real terms, which helps borrowers only when inflation is higher than lenders expected.