Why Rate Changes Do Not Affect Spending All at Once
A change in a central bank’s policy rate can influence market borrowing rates, but it does not instantly change every household’s mortgage payment or every firm’s investment plan. Some loans have fixed rates, some reset only on specified dates, and refinancing takes time and may involve costs. Firms may also need to review projects, obtain financing, and arrange purchases before spending changes. As a result, the effect on aggregate demand can be delayed and spread over time.
The size and timing of the response depend on the contract and the decision being made. A floating-rate borrower whose loan resets soon may experience a change quickly. A fixed-rate borrower may see no payment change unless refinancing is worthwhile. A business may face a lower borrowing rate but still postpone a project until its budget cycle or planning process allows it to proceed.
Where the Delays Arise
Several stages may separate a policy-rate change from a change in spending. Short-term market rates may adjust relatively quickly as expected policy paths change. Rates on longer-term loans can also reflect expected future rates, term premia, and credit spreads, so they need not move one-for-one with the current policy rate. Even if a market rate changes, a borrower’s contracted rate may remain fixed until a reset or refinancing.
The next delay is behavioral. A borrower may compare potential savings with fees, penalties, and the inconvenience of changing lenders. A firm may reconsider a project when financing costs change, but still need time to approve the project and put it into operation. Consequently, the response of total spending is typically a sequence of adjustments rather than a single immediate jump.
Market rates respond to policy changes and expectations, but the amount and timing vary by maturity and borrower risk.
A floating-rate loan may reset on a scheduled date; a fixed-rate loan generally does not change its rate automatically.
Households and firms weigh expected benefits against costs, uncertainty, and practical constraints.
Consumption or investment changes as borrowers act, so the effect on aggregate demand accumulates over time.
A Simple Model of Incomplete Pass-Through
A useful way to represent incomplete pass-through is to compare the change in a borrower’s rate with the policy-rate change. Let \(\Delta r^p\) denote the change in the policy rate and \(\Delta r^b\) the change in a particular borrower’s rate. In a simplified model, holding other influences such as credit risk and maturity constant, write:
Here \(\alpha_t\) is the fraction of the policy-rate change passed through to the borrower by time \(t\). If \(\alpha_t=0\), none has passed through by that time; if \(\alpha_t=1\), the borrower’s rate has moved by the full policy-rate change. Values between zero and one describe partial pass-through. This is a simplifying description, not a universal rule: market rates and borrower rates can move by more or less than the policy rate if expectations, spreads, or other conditions change.
For a loan with a constant balance \(B\), a rate change applying for a fraction \(q\) of a year changes simple interest by approximately \(B \Delta r^b q\). This calculation assumes the balance does not amortize during the period and interest is prorated using the annual rate; it does not describe a loan with compounding or changing balances.
Worked Example: A Floating-Rate Loan That Resets Midyear
A hypothetical borrower has a constant loan balance of $120,000 for one year. The annual rate is initially 8%. A policy-rate reduction of 1 percentage point is passed through at 60% to this borrower’s rate, but the contract does not reset until six months into the year. Assuming simple interest prorated by month, calculate the borrower’s interest for the year and compare it with the amount if the rate had not changed.
Method. First find the borrower’s rate reduction: \(0.60 \times 1\%=0.60\) percentage points. After the reset, the rate is \(8.00\%-0.60\%=7.40\%\). The first half-year remains at 8%; the second half-year is at 7.4%.
The first half-year’s interest is \(120{,}000 \times 0.08 \times 0.5=\$4{,}800\). The second half-year’s interest is \(120{,}000 \times 0.074 \times 0.5=\$4{,}440\). Total interest is \(\$4{,}800+\$4{,}440=\$9{,}240\).
With no rate change, full-year interest would be \(120{,}000 \times 0.08=\$9{,}600\). The borrower therefore saves \(\$9{,}600-\$9{,}240=\$360\). This is less than the \(\$720\) that a 0.60-percentage-point reduction would save over a full year, because the lower rate applies for only half the year.
Check and common mistake. The calculation uses a 0.60-percentage-point borrower-rate reduction, not the full 1-percentage-point policy change. It also applies the new rate only after the reset. Applying the new rate for the entire year would incorrectly calculate interest as \(\$8{,}880\).
Refinancing Adds a Decision Lag
A fixed-rate borrower does not automatically receive a lower payment when market rates fall. Refinancing may be possible, but the borrower must compare the value of lower future payments with fees, penalties, and the time remaining on the loan. Waiting to make that decision can reduce the number of periods in which savings are available.
Worked Example: Refinancing Now or Waiting
A hypothetical borrower has a $100,000 interest-only loan with two years remaining and an annual rate of 8%. The lender offers a two-year refinancing rate of 6%, with a $1,500 fee paid when refinancing occurs. There is no prepayment penalty, the principal remains $100,000, and interest is paid at each year-end. Use an annual effective discount rate of 5% to compare refinancing now with waiting one year. Assume the 6% offer remains available.
Method. Refinancing now reduces annual interest from \(100{,}000(0.08)=\$8{,}000\) to \(100{,}000(0.06)=\$6{,}000\). The saving is \(\$2{,}000\) at each of the next two year-ends. Discount those savings and subtract the immediate fee:
The first saving has present value \(2{,}000/1.05=\$1{,}904.76\). The second has present value \(2{,}000/1.1025=\$1{,}814.06\). The total present value of the savings is \(\$3{,}718.82\), so the net value of refinancing now is \(\$3{,}718.82-\$1{,}500=\$2{,}218.82\).
If the borrower waits one year, the first year’s interest remains at 8%. At the end of that year, refinancing leaves one year of savings: \(\$2{,}000\) at the second year-end. At the end of year one, the net value is \(2{,}000/1.05-1{,}500=\$404.76\). Discounting that amount back one year gives \(404.76/1.05=\$385.49\) at the original date.
Refinancing now has the greater modeled value: \(\$2{,}218.82\), compared with \(\$385.49\) for waiting. Check and common mistake: the fee is paid when refinancing occurs, while savings occur at year-end. Treating the fee as an annual cost or counting two years of savings after waiting would misstate the comparison. The result depends on the stated assumptions, including an unchanged offer and no penalty.
Investment Plans Also Adjust Gradually
A lower borrowing rate can improve a project’s net present value, but a firm may not immediately begin the project. It may need to update forecasts, obtain approval, or schedule equipment purchases. The effect of the lower rate on the project’s attractiveness and the timing of actual investment are therefore distinct.
For a project with an initial cost \(C_0\) and positive receipts \(C_t\) at the ends of periods \(t=1,\ldots,n\), discounted at an annual effective rate \(r\), net present value is:
When future receipts are positive, increasing \(r\) reduces each receipt’s present value. This can be seen by differentiating:
Each term in the sum is positive when \(C_t>0\) and \(r>-1\), so the derivative is negative. Thus, in this model, a lower discount rate raises NPV. The formula assumes the project’s cash flows are unchanged; if the project’s receipts or costs also respond to economic conditions, that separate effect must be modeled too.
Worked Example: A Lower Rate and a One-Year Investment Delay
A hypothetical project costs $51,000 at the start and pays $20,000 at each year-end for three years. Use annual effective discount rates of 9% and 7%. A firm can begin as soon as it approves the project, but its review process takes one year after the rate change. Calculate the NPV at both rates and the value today of the project NPV if the project begins one year from now. Assume the 7% rate applies throughout and the same cash-flow pattern begins when the project starts.
Method. First value the project at its start date. At 9%:
The three discounted receipts are \(\$18{,}348.62\), \(\$16{,}833.60\), and \(\$15{,}443.67\). Their sum is \(\$50{,}625.89\), giving an NPV of \(\$50{,}625.89-\$51{,}000=-\$374.11\), rounded to the nearest cent.
At 7%:
The discounted receipts are \(\$18{,}691.59\), \(\$17{,}468.77\), and \(\$16{,}325.96\). Their sum is \(\$52{,}486.32\), so the NPV is \(\$52{,}486.32-\$51{,}000=+\$1{,}486.32\), rounded to the nearest cent. The project changes from negative to positive NPV at these two rates.
Because the firm starts the project one year later, its NPV of \(\$1{,}486.32\) is measured at the start date one year from now. Its value today is \(1{,}486.32/1.07=\$1{,}389.08\), rounded to the nearest cent. The delay does not change the project’s NPV at its own start date under the stated assumptions, but it reduces the value today of that future NPV.
Check and common mistake. The cash flows occur at year-ends, so each receipt is discounted by its corresponding power of \(1+r\). The 9% NPV is \(-\$374.11\), not \(-\$374.13\); the calculation uses the stated cash flows and rounds only after summing the discounted receipts.
Why the Aggregate Effect Is Spread Out
At the level of the economy, different borrowers face different contracts, reset dates, fees, and investment schedules. Some react quickly; others do not react at all to a particular rate change. Even among borrowers whose rates fall, a smaller-than-full pass-through means that the change in their financing costs is less than the policy-rate movement. The resulting changes in consumption and investment therefore build over time rather than arriving simultaneously.
This does not mean every monetary-policy change has the same lag or that the response must follow a fixed schedule. Market rates can adjust before a policy move if expected changes are already reflected in prices. Contractual repricing and investment approvals can create later effects. Changes in credit spreads or other conditions may also offset or amplify the movement in a borrower’s rate. A sound analysis specifies which rate changed, how much was passed through, when the change applies, and when the spending decision occurs.
Common Errors
- Applying the policy-rate change directly to every loan. Borrower rates depend on pass-through, contract terms, and other influences. Identify the actual borrower-rate change before calculating interest savings.
- Ignoring the reset date. If a rate changes halfway through the year, apply the new rate only to the portion of the year after repricing, unless the contract says otherwise.
- Assuming fixed-rate payments adjust automatically. A fixed-rate borrower generally needs a refinancing decision, and refinancing may involve fees or penalties.
- Mixing the timing of fees and savings. Discount each cash flow from its actual payment date, and account for how waiting shortens the period of potential savings.
- Confusing a favorable NPV change with immediate investment. A project can become more attractive while approval, financing, or implementation remains delayed.
Check Your Understanding
For each problem, keep the stated timing and rate assumptions separate from the size of the policy-rate change.
- A hypothetical $80,000 floating-rate loan has a constant balance for one year and charges simple interest prorated by time. Its rate is 9% for the first three months, then resets to 8.5% for the remaining nine months. What is the year’s interest, and how much is saved compared with a 9% rate all year? (Answer: Interest is $6,900; savings are $300.)
- A lender passes through 75% of a 0.8-percentage-point policy-rate decrease to a borrower whose $50,000 balance remains constant. The loan rate is 7.4% for the first half-year and resets for the second half; use simple interest prorated by time. What is the new rate and the total interest for the year? (Answer: New rate is 6.8%; total interest is $3,550.)
- A hypothetical borrower has a $60,000 interest-only loan with two years remaining at 7.5%. Refinancing reduces the rate to 6.5%, costs $900 immediately, and has no penalty. Interest savings are paid at each year-end. At a 4% annual effective discount rate, what is the net present value of refinancing now? (Answer: \(600/1.04+600/1.04^2-900=\$231.66\).)
- A project costs $40,000 and pays $15,000 at each year-end for three years. Calculate its NPV at annual effective rates of 8% and 6%. If the project begins one year after the rate falls to 6%, what is the project NPV’s value today? (Answer: NPV at 8% is \(-\$1,343.55\); at 6% it is \(+\$95.18\); the delayed NPV is worth \(95.18/1.06=\$89.79\) today.)