Compare money returns with purchasing power

Compare money returns with purchasing power

Start with the question

Does a larger balance always buy more?

Inspect the teaching record

A fictional deposit begins at 100 credits and pays 10% over one year. A basket costing 100 at the start costs 105 at the end. Ignore taxes, fees and risk for this calculation.

This is fictional teaching evidence. It is not an observation about an actual community or economy.

Explain the mechanism

Nominal interest changes the money balance. A real return adjusts for changes in purchasing power. Subtracting inflation is a useful approximation for small rates; dividing growth factors gives the exact one-period comparison. This exercise is not a recommendation about actual financial products.

Follow the worked example

Balance becomes 110. It buys 110/105 ≈ 1.0476 baskets, a real gain of about 4.76%. The shortcut 10%−5%=5% is close but not exact.

Challenge the first explanation

A sales pitch calls the whole 10% increase a gain in purchasing power. The future inflation rate was not known at the start; an expected real return can differ from the realized one.

Make and revise your evidence

Write both nominal and real calculations. Explain how unexpected inflation changes the borrower/lender comparison without claiming every contract is identical.

Revise your answer to “Does a larger balance always buy more?” using both source IDs. Separate the checked calculation from a judgment, and identify evidence that could reverse your judgment.

Name the idea

Real return: Change in purchasing power after adjusting a money return for price changes.

Assumption: A condition accepted for a model or argument; it needs justification before applying the result elsewhere.

Extend the investigation

Independently extend the investigation “Compare money returns with purchasing power” with a documented real dataset or scholarly source. Preserve definitions, recreate one calculation or evidence table, compare a rival explanation and report why the teaching example cannot establish the real-world conclusion.

Compare the same expected repayment under two contracts

The deposit above illustrates purchasing power. Now keep expectations and the initial loan amount the same while changing the contract rule. Do not compare two different interest promises and attribute the whole difference to inflation.

Hold the contract fixed while prices surprise

Two fictional one-year loans each advance 100 credits. At signing, both sides expect 5% inflation and compare a 4% real return. Ignore fees, taxes, default, timing differences and all other income. The base price index is 100.

Predict: if inflation is higher than expected, will a fixed promise buy more or less than expected at repayment? Then test unexpected deflation.

Actual inflation over the year-5%0%5%10%

The fixed contract promises 100 × 1.04 × 1.05 = 109.20 nominal credits, a 9.2% nominal rate. The indexed contract promises 104 base-year credits; its nominal payment changes with the actual price index. These contracts match at the expected 5% inflation.

Price index at repayment: 105.00. Only actual inflation changes.

Contract	Nominal repayment	Repayment in base-year credits	Real return on 100
Fixed nominal	109.20	104.00	4.00%
Fully indexed	109.20	104.00	4.00%

Fixed real repayment = 109.20 ÷ 1.05 = 104.00 base-year credits. Indexed nominal repayment = 104 × 1.05 = 109.20; dividing by the same price factor returns 104.

Fixed contract: real repayment is 104.00 base-year credits, compared with the expected 104. The expected purchasing-power repayment is realized.

The lender’s receipt and borrower’s payment are the same transfer, viewed from opposite sides. A lower real repayment is not proof of a borrower’s overall gain: wages, job loss and other prices are absent. Nor is it a resource saving for the economy. Full indexation stabilizes repayment in this chosen index, not every household’s own basket.

Compare −5%, 5% and 10%. State the fixed nominal promise, expected real repayment and actual real repayment each time. Explain why the indexed nominal payment can fall below 100 during deflation while still delivering a positive real return.

Restore expected inflation

These are ideal teaching contracts. Actual indexing may have caps, floors, lags or different indices. This temporary control resets on reload, is excluded from captures and awards no mastery. Save inputs and reasoning in the source notebook.

The exact one-period relationship is 1 + nominal rate = (1 + real rate) × (1 + inflation), using rates as fractions. At signing, substitute the expected inflation rate to construct this hypothetical nominal promise: 1.04×1.05−1 = 0.092, or 9.2%. After the year, use actual inflation to calculate the realized real return. The common shortcut “nominal minus inflation” omits their interaction and is an approximation.

At actual inflation of 10%, the fixed repayment buys 109.2/1.10 ≈ 99.27 base-year credits. That is less than the initial 100 and less than the expected 104. At actual deflation of 5%, it buys 109.2/0.95 ≈ 114.95, above the expected 104. In both cases the nominal contract still requires 109.20; the real value changes.

The indexed promise delivers 104 base-year credits under each selected price scenario. With 5% deflation it requires 98.80 nominal credits: 98.8/0.95=104. A nominal payment below the original 100 can therefore still give a positive real return when money buys more. This is an ideal symmetric indexing rule, not a description of every actual loan.

Account for incidence without claiming everyone gains or loses

Write a two-sided ledger: the lender receives exactly what the borrower pays. Compare each realized real amount with the expected 104. Unexpected inflation reduces that fixed nominal repayment’s purchasing power; unexpected deflation raises it. Those statements concern this contract. They do not establish the parties’ total gains after wage changes, unemployment, taxes, other assets or default.

A fixed nominal pension or wage can also lose purchasing power when prices rise faster than expected. An indexed payment may behave differently. Inflation can require repricing and make nominal comparisons harder, but these effects need their own evidence; they cannot be estimated by adding the loan’s transfer to both parties as a social resource cost.

Transfer: repair a surprising claim

A new fictional one-year loan advances 200 credits and promises a fixed 216 at repayment. Both sides expected inflation of 4%; actual inflation is −2%. Calculate expected and actual repayment in initial-price purchasing power, the realized real return, and who faces the higher real obligation relative to expectation. Then state the nominal payment for an indexed contract promising the same expected real repayment.

Check the repayment transfer

Expected real repayment = 216/1.04 ≈ 207.6923. Actual fixed real repayment = 216/0.98 ≈ 220.4082. The realized real return is approximately 10.2041%, not the nominal 8%. The fixed contract transfers about 12.7159 more base-year credits from borrower to lender than expected.

A fully indexed contract matching the expected real repayment would instead require (216/1.04)×0.98 ≈ 203.5385 nominal credits and deliver about 207.6923 base-year credits. This preserves the original expected real payment; it does not silently substitute a different promised real return. Actual contractual rounding is outside this unrounded teaching calculation.

For high-school practice, keep nominal and real units in separate ledger columns. AP practice should explain unexpected inflation and deflation for an unfamiliar fixed contract, distinguishing expected from realized returns. Introductory-college practice should also examine an actual indexing clause’s reference series, timing and limits before claiming its purchasing power is protected. No financial-product recommendation follows from these fictional contracts.

Read the floor clause before applying it

The ideal indexed loan above is symmetric. Treasury's TIPS documentation describes a different contract: interest follows adjusted principal, while redemption at maturity has an original-face-value floor. Interpret the clauses before using the word “protected.”

Prediction: which payment does the floor protect?

Read the documented terms and their scope

• Interest rule: the fixed annual coupon rate is applied to inflation-adjusted principal, with payments every six months.
• Maturity rule: principal redemption is the larger of adjusted principal and original face value.
• Early sale: proceeds depend on the market value; the maturity rule does not supply an early-sale quote.
• Index timing: the reference CPI uses a lagged month and daily interpolation. A contemporaneous inflation headline is not automatically the security's index ratio.

Sources: TreasuryDirect TIPS terms and FS Publication0042, revised March2019. These are descriptions of actual terms; the amounts and ratios below are original teaching inputs. Consult an issue's actual dates and index-ratio records for an actual payment.

Original example: face value1,000, annual coupon2%, a full six-month coupon period. Select a supplied index ratio, not an annual inflation rate. An index ratio0.90 makes adjusted principal900; it does not mean90% inflation. No specific security, observed price or investment return is represented.

Supplied index ratio0.800.901.001.101.20 Contract eventScheduled coupon before maturityMaturity: principal plus final couponEarly sale: no market quote supplied Hypothetical purchase-price comparison1,0001,100: premium-price transfer

Original contract arithmetic, selected event: maturity

Quantity	Value	Rule and limitation
Adjusted principal	900.00	1,000×0.90; do not apply the maturity floor here
Full-period coupon at this ratio	9.00	900.00×0.02/2; not an early-sale accrued-interest quote
Principal paid at selected event	1000.00	max(1,000, adjusted principal)
Interest paid at selected event	9.00	Full semiannual coupon, including at maturity
Selected-event cash amount	1009.00	Principal paid plus coupon; not total lifetime return

The floor adds 100.00 to adjusted principal for redemption, leaving the coupon base unchanged. Principal redemption minus hypothetical purchase price1000 is 0.00. This excludes every coupon and cost; it is not profit or total return.

Transfer: set ratio0.80 and purchase price1,100, then compare coupon-only, maturity and early sale. Repair the statement “the original-face floor guarantees recovery of any purchase price and every coupon is at least10.” Identify which additional records a complete return calculation needs.

Revised clause interpretation and transfer

Compare your contract reading

At ratio0.90, adjusted principal900 gives coupon9. Maturity returns principal1,000 plus9, not a coupon of10. At ratio0.80 the coupon is8 and maturity cash1,008; principal alone is100 below a purchase price of1,100. This does not calculate the holder's overall loss, because earlier coupons and costs are omitted. The early-sale price remains unknown. Above ratio1, principal redemption follows the larger adjusted principal; the original-face floor is inactive.

Copy your indexed-contract analysis

{ "activity": "MAC-02.d indexed principal floor", "audit": { "ratio": 0.9, "event": "maturity", "purchase": 1000, "face": 1000, "annualRate": 0.02, "adjusted": 900, "coupon": 9, "maturityPrincipal": 1000, "floorTopUp": 100, "principalPaid": 1000, "interestPaid": 9, "cashPaid": 1009, "principalMinusPurchase": 0 }, "worksheet": { "prediction": "", "revision": "" }, "feedbackSeen": false, "limits": "Treasury TIPS clause illustration using original1000 face,2% annual coupon and supplied ratios; not an actual issue or quote. Full semiannual coupon only. Original face floor applies to maturity principal, not coupon base or market sale price. Daily CPI lag/interpolation, rounding, accrued interest, taxes, fees, previous coupons and total return not modeled. Purchase comparison concerns principal alone. Temporary practice." }

Reset indexed-floor practice

Temporary practice: reset restores ratio0.90/maturity/price1,000 and clears writing, retaining guide/report exposure during this visit. Reload clears work and exposure. This is contract-literacy practice, not a verified independent assessment.