Research question and design
When does a nominal-versus-real present-value comparison preserve consistent units, and how do inflation assumptions change future purchasing units? All 135 cases are shown below: three horizons, three annual cashflow amounts, three nominal rates and five inflation assumptions. Values are generic units, not a security or currency quote.
Assumptions
Fixed annual nominal payments of 0, 3 or 7 generic units, plus a terminal payment of 100, occur over 2, 5 or 10 years. Nominal discount rates are assumed at 3%, 5% or 7%; inflation at 0%, 2%, 4%, 6% or 8%. Annual compounding and certain cashflows are assumed. Observed CPI is not used as forward inflation or a model forecast.
Methods and units
Real discount rate = (1 + nominal rate) / (1 + assumed inflation) − 1. Real cashflow at year t = nominal cashflow / (1 + assumed inflation)^t. Present value sums each cashflow divided by its consistent discount factor. Intermediate Decimal precision is 50; the retained outputs are reported to eight decimal places. The real-rate column is a decimal fraction, not a percentage.
How to read the results
With fixed nominal cashflows and consistently deflated cashflows/real rates, nominal and real present values agree at the same base date. This is a change-of-units identity, not evidence that inflation has no economic effect. Terminal purchasing units decline as the inflation assumption rises. Mixing nominal cashflows with a real rate without deflation would break unit consistency. No future investment return follows from this identity.
2-year cases
Wide tables scroll horizontally. Focus a table and use the left and right arrow keys to read all columns.
| Case | Annual nominal amount | Assumed nominal rate | Assumed inflation | Real rate, decimal | Nominal PV | Real PV, base-date units | Terminal 100 purchasing units |
|---|---|---|---|---|---|---|---|
| 001 | 0 | 3.00% | 0% | 0.03000000 | 94.25959091 | 94.25959091 | 100.00000000 |
| 002 | 0 | 3.00% | 2.00% | 0.00980392 | 94.25959091 | 94.25959091 | 96.11687812 |
| 003 | 0 | 3.00% | 4.00% | -0.00961538 | 94.25959091 | 94.25959091 | 92.45562130 |
| 004 | 0 | 3.00% | 6.00% | -0.02830189 | 94.25959091 | 94.25959091 | 88.99964400 |
| 005 | 0 | 3.00% | 8.00% | -0.04629630 | 94.25959091 | 94.25959091 | 85.73388203 |
| 006 | 0 | 5.00% | 0% | 0.05000000 | 90.70294785 | 90.70294785 | 100.00000000 |
| 007 | 0 | 5.00% | 2.00% | 0.02941176 | 90.70294785 | 90.70294785 | 96.11687812 |
| 008 | 0 | 5.00% | 4.00% | 0.00961538 | 90.70294785 | 90.70294785 | 92.45562130 |
| 009 | 0 | 5.00% | 6.00% | -0.00943396 | 90.70294785 | 90.70294785 | 88.99964400 |
| 010 | 0 | 5.00% | 8.00% | -0.02777778 | 90.70294785 | 90.70294785 | 85.73388203 |
| 011 | 0 | 7.00% | 0% | 0.07000000 | 87.34387283 | 87.34387283 | 100.00000000 |
| 012 | 0 | 7.00% | 2.00% | 0.04901961 | 87.34387283 | 87.34387283 | 96.11687812 |
| 013 | 0 | 7.00% | 4.00% | 0.02884615 | 87.34387283 | 87.34387283 | 92.45562130 |
| 014 | 0 | 7.00% | 6.00% | 0.00943396 | 87.34387283 | 87.34387283 | 88.99964400 |
| 015 | 0 | 7.00% | 8.00% | -0.00925926 | 87.34387283 | 87.34387283 | 85.73388203 |
| 016 | 3 | 3.00% | 0% | 0.03000000 | 100.00000000 | 100.00000000 | 100.00000000 |
| 017 | 3 | 3.00% | 2.00% | 0.00980392 | 100.00000000 | 100.00000000 | 96.11687812 |
| 018 | 3 | 3.00% | 4.00% | -0.00961538 | 100.00000000 | 100.00000000 | 92.45562130 |
| 019 | 3 | 3.00% | 6.00% | -0.02830189 | 100.00000000 | 100.00000000 | 88.99964400 |
| 020 | 3 | 3.00% | 8.00% | -0.04629630 | 100.00000000 | 100.00000000 | 85.73388203 |
| 021 | 3 | 5.00% | 0% | 0.05000000 | 96.28117914 | 96.28117914 | 100.00000000 |
| 022 | 3 | 5.00% | 2.00% | 0.02941176 | 96.28117914 | 96.28117914 | 96.11687812 |
| 023 | 3 | 5.00% | 4.00% | 0.00961538 | 96.28117914 | 96.28117914 | 92.45562130 |
| 024 | 3 | 5.00% | 6.00% | -0.00943396 | 96.28117914 | 96.28117914 | 88.99964400 |
| 025 | 3 | 5.00% | 8.00% | -0.02777778 | 96.28117914 | 96.28117914 | 85.73388203 |
| 026 | 3 | 7.00% | 0% | 0.07000000 | 92.76792733 | 92.76792733 | 100.00000000 |
| 027 | 3 | 7.00% | 2.00% | 0.04901961 | 92.76792733 | 92.76792733 | 96.11687812 |
| 028 | 3 | 7.00% | 4.00% | 0.02884615 | 92.76792733 | 92.76792733 | 92.45562130 |
| 029 | 3 | 7.00% | 6.00% | 0.00943396 | 92.76792733 | 92.76792733 | 88.99964400 |
| 030 | 3 | 7.00% | 8.00% | -0.00925926 | 92.76792733 | 92.76792733 | 85.73388203 |
| 031 | 7 | 3.00% | 0% | 0.03000000 | 107.65387878 | 107.65387878 | 100.00000000 |
| 032 | 7 | 3.00% | 2.00% | 0.00980392 | 107.65387878 | 107.65387878 | 96.11687812 |
| 033 | 7 | 3.00% | 4.00% | -0.00961538 | 107.65387878 | 107.65387878 | 92.45562130 |
| 034 | 7 | 3.00% | 6.00% | -0.02830189 | 107.65387878 | 107.65387878 | 88.99964400 |
| 035 | 7 | 3.00% | 8.00% | -0.04629630 | 107.65387878 | 107.65387878 | 85.73388203 |
| 036 | 7 | 5.00% | 0% | 0.05000000 | 103.71882086 | 103.71882086 | 100.00000000 |
| 037 | 7 | 5.00% | 2.00% | 0.02941176 | 103.71882086 | 103.71882086 | 96.11687812 |
| 038 | 7 | 5.00% | 4.00% | 0.00961538 | 103.71882086 | 103.71882086 | 92.45562130 |
| 039 | 7 | 5.00% | 6.00% | -0.00943396 | 103.71882086 | 103.71882086 | 88.99964400 |
| 040 | 7 | 5.00% | 8.00% | -0.02777778 | 103.71882086 | 103.71882086 | 85.73388203 |
| 041 | 7 | 7.00% | 0% | 0.07000000 | 100.00000000 | 100.00000000 | 100.00000000 |
| 042 | 7 | 7.00% | 2.00% | 0.04901961 | 100.00000000 | 100.00000000 | 96.11687812 |
| 043 | 7 | 7.00% | 4.00% | 0.02884615 | 100.00000000 | 100.00000000 | 92.45562130 |
| 044 | 7 | 7.00% | 6.00% | 0.00943396 | 100.00000000 | 100.00000000 | 88.99964400 |
| 045 | 7 | 7.00% | 8.00% | -0.00925926 | 100.00000000 | 100.00000000 | 85.73388203 |
5-year cases
Wide tables scroll horizontally. Focus a table and use the left and right arrow keys to read all columns.
| Case | Annual nominal amount | Assumed nominal rate | Assumed inflation | Real rate, decimal | Nominal PV | Real PV, base-date units | Terminal 100 purchasing units |
|---|---|---|---|---|---|---|---|
| 046 | 0 | 3.00% | 0% | 0.03000000 | 86.26087844 | 86.26087844 | 100.00000000 |
| 047 | 0 | 3.00% | 2.00% | 0.00980392 | 86.26087844 | 86.26087844 | 90.57308098 |
| 048 | 0 | 3.00% | 4.00% | -0.00961538 | 86.26087844 | 86.26087844 | 82.19271068 |
| 049 | 0 | 3.00% | 6.00% | -0.02830189 | 86.26087844 | 86.26087844 | 74.72581729 |
| 050 | 0 | 3.00% | 8.00% | -0.04629630 | 86.26087844 | 86.26087844 | 68.05831970 |
| 051 | 0 | 5.00% | 0% | 0.05000000 | 78.35261665 | 78.35261665 | 100.00000000 |
| 052 | 0 | 5.00% | 2.00% | 0.02941176 | 78.35261665 | 78.35261665 | 90.57308098 |
| 053 | 0 | 5.00% | 4.00% | 0.00961538 | 78.35261665 | 78.35261665 | 82.19271068 |
| 054 | 0 | 5.00% | 6.00% | -0.00943396 | 78.35261665 | 78.35261665 | 74.72581729 |
| 055 | 0 | 5.00% | 8.00% | -0.02777778 | 78.35261665 | 78.35261665 | 68.05831970 |
| 056 | 0 | 7.00% | 0% | 0.07000000 | 71.29861795 | 71.29861795 | 100.00000000 |
| 057 | 0 | 7.00% | 2.00% | 0.04901961 | 71.29861795 | 71.29861795 | 90.57308098 |
| 058 | 0 | 7.00% | 4.00% | 0.02884615 | 71.29861795 | 71.29861795 | 82.19271068 |
| 059 | 0 | 7.00% | 6.00% | 0.00943396 | 71.29861795 | 71.29861795 | 74.72581729 |
| 060 | 0 | 7.00% | 8.00% | -0.00925926 | 71.29861795 | 71.29861795 | 68.05831970 |
| 061 | 3 | 3.00% | 0% | 0.03000000 | 100.00000000 | 100.00000000 | 100.00000000 |
| 062 | 3 | 3.00% | 2.00% | 0.00980392 | 100.00000000 | 100.00000000 | 90.57308098 |
| 063 | 3 | 3.00% | 4.00% | -0.00961538 | 100.00000000 | 100.00000000 | 82.19271068 |
| 064 | 3 | 3.00% | 6.00% | -0.02830189 | 100.00000000 | 100.00000000 | 74.72581729 |
| 065 | 3 | 3.00% | 8.00% | -0.04629630 | 100.00000000 | 100.00000000 | 68.05831970 |
| 066 | 3 | 5.00% | 0% | 0.05000000 | 91.34104666 | 91.34104666 | 100.00000000 |
| 067 | 3 | 5.00% | 2.00% | 0.02941176 | 91.34104666 | 91.34104666 | 90.57308098 |
| 068 | 3 | 5.00% | 4.00% | 0.00961538 | 91.34104666 | 91.34104666 | 82.19271068 |
| 069 | 3 | 5.00% | 6.00% | -0.00943396 | 91.34104666 | 91.34104666 | 74.72581729 |
| 070 | 3 | 5.00% | 8.00% | -0.02777778 | 91.34104666 | 91.34104666 | 68.05831970 |
| 071 | 3 | 7.00% | 0% | 0.07000000 | 83.59921026 | 83.59921026 | 100.00000000 |
| 072 | 3 | 7.00% | 2.00% | 0.04901961 | 83.59921026 | 83.59921026 | 90.57308098 |
| 073 | 3 | 7.00% | 4.00% | 0.02884615 | 83.59921026 | 83.59921026 | 82.19271068 |
| 074 | 3 | 7.00% | 6.00% | 0.00943396 | 83.59921026 | 83.59921026 | 74.72581729 |
| 075 | 3 | 7.00% | 8.00% | -0.00925926 | 83.59921026 | 83.59921026 | 68.05831970 |
| 076 | 7 | 3.00% | 0% | 0.03000000 | 118.31882875 | 118.31882875 | 100.00000000 |
| 077 | 7 | 3.00% | 2.00% | 0.00980392 | 118.31882875 | 118.31882875 | 90.57308098 |
| 078 | 7 | 3.00% | 4.00% | -0.00961538 | 118.31882875 | 118.31882875 | 82.19271068 |
| 079 | 7 | 3.00% | 6.00% | -0.02830189 | 118.31882875 | 118.31882875 | 74.72581729 |
| 080 | 7 | 3.00% | 8.00% | -0.04629630 | 118.31882875 | 118.31882875 | 68.05831970 |
| 081 | 7 | 5.00% | 0% | 0.05000000 | 108.65895334 | 108.65895334 | 100.00000000 |
| 082 | 7 | 5.00% | 2.00% | 0.02941176 | 108.65895334 | 108.65895334 | 90.57308098 |
| 083 | 7 | 5.00% | 4.00% | 0.00961538 | 108.65895334 | 108.65895334 | 82.19271068 |
| 084 | 7 | 5.00% | 6.00% | -0.00943396 | 108.65895334 | 108.65895334 | 74.72581729 |
| 085 | 7 | 5.00% | 8.00% | -0.02777778 | 108.65895334 | 108.65895334 | 68.05831970 |
| 086 | 7 | 7.00% | 0% | 0.07000000 | 100.00000000 | 100.00000000 | 100.00000000 |
| 087 | 7 | 7.00% | 2.00% | 0.04901961 | 100.00000000 | 100.00000000 | 90.57308098 |
| 088 | 7 | 7.00% | 4.00% | 0.02884615 | 100.00000000 | 100.00000000 | 82.19271068 |
| 089 | 7 | 7.00% | 6.00% | 0.00943396 | 100.00000000 | 100.00000000 | 74.72581729 |
| 090 | 7 | 7.00% | 8.00% | -0.00925926 | 100.00000000 | 100.00000000 | 68.05831970 |
10-year cases
Wide tables scroll horizontally. Focus a table and use the left and right arrow keys to read all columns.
| Case | Annual nominal amount | Assumed nominal rate | Assumed inflation | Real rate, decimal | Nominal PV | Real PV, base-date units | Terminal 100 purchasing units |
|---|---|---|---|---|---|---|---|
| 091 | 0 | 3.00% | 0% | 0.03000000 | 74.40939149 | 74.40939149 | 100.00000000 |
| 092 | 0 | 3.00% | 2.00% | 0.00980392 | 74.40939149 | 74.40939149 | 82.03482999 |
| 093 | 0 | 3.00% | 4.00% | -0.00961538 | 74.40939149 | 74.40939149 | 67.55641688 |
| 094 | 0 | 3.00% | 6.00% | -0.02830189 | 74.40939149 | 74.40939149 | 55.83947769 |
| 095 | 0 | 3.00% | 8.00% | -0.04629630 | 74.40939149 | 74.40939149 | 46.31934881 |
| 096 | 0 | 5.00% | 0% | 0.05000000 | 61.39132535 | 61.39132535 | 100.00000000 |
| 097 | 0 | 5.00% | 2.00% | 0.02941176 | 61.39132535 | 61.39132535 | 82.03482999 |
| 098 | 0 | 5.00% | 4.00% | 0.00961538 | 61.39132535 | 61.39132535 | 67.55641688 |
| 099 | 0 | 5.00% | 6.00% | -0.00943396 | 61.39132535 | 61.39132535 | 55.83947769 |
| 100 | 0 | 5.00% | 8.00% | -0.02777778 | 61.39132535 | 61.39132535 | 46.31934881 |
| 101 | 0 | 7.00% | 0% | 0.07000000 | 50.83492921 | 50.83492921 | 100.00000000 |
| 102 | 0 | 7.00% | 2.00% | 0.04901961 | 50.83492921 | 50.83492921 | 82.03482999 |
| 103 | 0 | 7.00% | 4.00% | 0.02884615 | 50.83492921 | 50.83492921 | 67.55641688 |
| 104 | 0 | 7.00% | 6.00% | 0.00943396 | 50.83492921 | 50.83492921 | 55.83947769 |
| 105 | 0 | 7.00% | 8.00% | -0.00925926 | 50.83492921 | 50.83492921 | 46.31934881 |
| 106 | 3 | 3.00% | 0% | 0.03000000 | 100.00000000 | 100.00000000 | 100.00000000 |
| 107 | 3 | 3.00% | 2.00% | 0.00980392 | 100.00000000 | 100.00000000 | 82.03482999 |
| 108 | 3 | 3.00% | 4.00% | -0.00961538 | 100.00000000 | 100.00000000 | 67.55641688 |
| 109 | 3 | 3.00% | 6.00% | -0.02830189 | 100.00000000 | 100.00000000 | 55.83947769 |
| 110 | 3 | 3.00% | 8.00% | -0.04629630 | 100.00000000 | 100.00000000 | 46.31934881 |
| 111 | 3 | 5.00% | 0% | 0.05000000 | 84.55653014 | 84.55653014 | 100.00000000 |
| 112 | 3 | 5.00% | 2.00% | 0.02941176 | 84.55653014 | 84.55653014 | 82.03482999 |
| 113 | 3 | 5.00% | 4.00% | 0.00961538 | 84.55653014 | 84.55653014 | 67.55641688 |
| 114 | 3 | 5.00% | 6.00% | -0.00943396 | 84.55653014 | 84.55653014 | 55.83947769 |
| 115 | 3 | 5.00% | 8.00% | -0.02777778 | 84.55653014 | 84.55653014 | 46.31934881 |
| 116 | 3 | 7.00% | 0% | 0.07000000 | 71.90567384 | 71.90567384 | 100.00000000 |
| 117 | 3 | 7.00% | 2.00% | 0.04901961 | 71.90567384 | 71.90567384 | 82.03482999 |
| 118 | 3 | 7.00% | 4.00% | 0.02884615 | 71.90567384 | 71.90567384 | 67.55641688 |
| 119 | 3 | 7.00% | 6.00% | 0.00943396 | 71.90567384 | 71.90567384 | 55.83947769 |
| 120 | 3 | 7.00% | 8.00% | -0.00925926 | 71.90567384 | 71.90567384 | 46.31934881 |
| 121 | 7 | 3.00% | 0% | 0.03000000 | 134.12081135 | 134.12081135 | 100.00000000 |
| 122 | 7 | 3.00% | 2.00% | 0.00980392 | 134.12081135 | 134.12081135 | 82.03482999 |
| 123 | 7 | 3.00% | 4.00% | -0.00961538 | 134.12081135 | 134.12081135 | 67.55641688 |
| 124 | 7 | 3.00% | 6.00% | -0.02830189 | 134.12081135 | 134.12081135 | 55.83947769 |
| 125 | 7 | 3.00% | 8.00% | -0.04629630 | 134.12081135 | 134.12081135 | 46.31934881 |
| 126 | 7 | 5.00% | 0% | 0.05000000 | 115.44346986 | 115.44346986 | 100.00000000 |
| 127 | 7 | 5.00% | 2.00% | 0.02941176 | 115.44346986 | 115.44346986 | 82.03482999 |
| 128 | 7 | 5.00% | 4.00% | 0.00961538 | 115.44346986 | 115.44346986 | 67.55641688 |
| 129 | 7 | 5.00% | 6.00% | -0.00943396 | 115.44346986 | 115.44346986 | 55.83947769 |
| 130 | 7 | 5.00% | 8.00% | -0.02777778 | 115.44346986 | 115.44346986 | 46.31934881 |
| 131 | 7 | 7.00% | 0% | 0.07000000 | 100.00000000 | 100.00000000 | 100.00000000 |
| 132 | 7 | 7.00% | 2.00% | 0.04901961 | 100.00000000 | 100.00000000 | 82.03482999 |
| 133 | 7 | 7.00% | 4.00% | 0.02884615 | 100.00000000 | 100.00000000 | 67.55641688 |
| 134 | 7 | 7.00% | 6.00% | 0.00943396 | 100.00000000 | 100.00000000 | 55.83947769 |
| 135 | 7 | 7.00% | 8.00% | -0.00925926 | 100.00000000 | 100.00000000 | 46.31934881 |
Research-only boundaries
Flat assumed rates and fixed certain payments omit taxes, fees, default, credit spread, liquidity and uncertain cashflows. No instrument, portfolio, strategy performance, predictive validation, backtest, recommendation, ranking, allocation, order or execution is supplied. Independent model and customer-value acceptance remain unissued. The earlier nominal-rate sensitivity and haircut study is separate; no existing validation suite was rerun to assemble these cases.
Methods provenance and corrections
The displayed cases are copied from the preserved V2 nominal/real study and its pure research methods, not newly calibrated from macro releases. The companion manifest retains their exact original hashes. A numerical correction requires a successor with changed inputs, methods and dependent outputs identified; this local edition is not an independent model review.