Real Interest Rate (Fisher Equation) Calculator
The interest your bank quotes is the nominal rate — but inflation chips away at the actual purchasing power you get back. Enter a nominal rate and an inflation rate to see the exact real return via the Fisher equation (1 + real) = (1 + nominal) ÷ (1 + inflation), alongside the textbook approximation r ≈ i − π so you can see at a glance whether you are truly outrunning prices.
Please enter a valid number
Real rate (exact, Fisher)
2.94%
Net gain in purchasing power — the nominal return outpaces inflation.
Approximation r ≈ i − π
3.00%
Exact − approx
−0.06pp
Fisher equation: (1 + real) = (1 + nominal) ÷ (1 + inflation)
When inflation is low (< 5%), the linear approximation r ≈ i − π is close to the exact value, which is why everyday financial commentary just subtracts. The gap widens as inflation grows, so prefer the exact value when either rate is large.
Formula
Real rate r = (1 + nominal i) ÷ (1 + inflation π) − 1 Approx. r ≈ i − π (accurate when both are small)
- · Introduced by Irving Fisher in The Theory of Interest (1930) — the "real" rate is the growth of purchasing power after stripping out inflation.
- · At low inflation the linear approximation r ≈ i − π is very close to the exact value (≈ 0.06 pp gap when i = 5 %, π = 2 %), which is why everyday news commentary just subtracts the two.
- · The gap grows with the rates — e.g. i = 8 %, π = 12 % gives an approx of −4 % but an exact value of −3.57 % (0.43 pp gap). Use the exact value for serious financial analysis.
- · Real rates can be ex-post (using realised inflation) or ex-ante (using expected inflation). Retail HK users often pair the HKMA-published bank time-deposit rates against the Census & Statistics Department Composite CPI.
- · Inflation-linked instruments — US TIPS, UK Index-linked Gilts, Hong Kong iBond — pay a coupon explicitly tied to CPI, so they target a real yield directly.
- · Negative inputs are allowed: deflation (negative inflation) raises the real rate; some developed-market policy rates have briefly gone negative too. The only forbidden case is inflation = −100 %, which makes the denominator zero.
- · Tax is ignored — to get an after-tax real rate, first compute i_after = i × (1 − tax rate) and use that as the nominal input.
Frequently asked
Why not just subtract inflation from the nominal rate?
You can — that is the textbook Fisher approximation r ≈ i − π, and when both rates are small (< 5 %) the gap with the exact value is usually under 0.1 pp, which is why most news commentary just subtracts. The gap widens at high inflation: nominal 8 %, inflation 12 % gives an approx of −4 % but an exact value of −3.57 % (0.43 pp gap). For retirement or long-horizon planning, prefer the exact value.
My time deposit pays 3.5 % and inflation is 2.5 % — is my real return 1 %?
Almost — the exact value is (1.035 ÷ 1.025) − 1 ≈ 0.976 %, and the approximation gives 1 %, a gap of about 0.024 pp. That is the pre-tax real return. Hong Kong does not withhold tax on local bank interest, but offshore deposits and bond coupons are usually taxable, which trims another 10–17 %. Also check whether the inflation assumption matches your personal basket — housing, private healthcare and education tend to run hotter than headline CPI.
Real rates can go negative — does that mean I am losing money?
Yes — when inflation outpaces the nominal rate, the real rate goes negative and the purchasing power of the principal shrinks. In 2022, with US CPI at 8–9 % while savings accounts still paid near zero, depositors faced a real rate of roughly −5 %, meaning $100 in the account could buy only about $95 worth of goods a year later. Typical responses: inflation-linked instruments (iBond / TIPS / HK Silver Bond), longer-tenor deposits, or reallocating into other asset classes.
Hong Kong iBond already pays a CPI-linked coupon — is this calculator still useful?
Still useful: iBond pays the greater of a guaranteed floor and the average Composite CPI, so its actual yield outpaces CPI in low-inflation years and tracks CPI in high-inflation years. To compare a regular bank time deposit or any other instrument on the same footing, you still need the Fisher equation — plug in your nominal rate and the expected inflation to compare real yields apples-to-apples.
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