Influences on households' spending, saving and borrowing: rate of interest

Households – How the Rate of Interest Influences Spending, Saving and Borrowing

1. What the Cambridge 0455 syllabus expects (Section 3.2 – Households)

2. The five influences on household decisions

All five factors operate simultaneously (Cambridge wording). Each can reinforce or offset the others.

• Income (disposable income) – A rise in income increases the amount of money that can be allocated to current consumption, saving or repayment of debt. Higher income therefore tends to raise both spending and saving, although the exact split depends on the other influences.
• Rate of interest – The focus of this note; see Sections 3‑7.
• Consumer confidence – When households feel optimistic about future earnings and the economy, they are more willing to spend now and to take on debt. Low confidence encourages precautionary saving even if interest rates are low.
• Age and life‑stage – Younger households usually have a long time‑horizon, so they are more inclined to borrow for house purchase or education and to spend a larger share of income. Older households, especially those approaching retirement, tend to save more and borrow less, prioritising wealth preservation.
• Cultural & social factors – Attitudes toward debt, thrift, and consumption differ between societies. For example, cultures that value frugality may limit borrowing even when rates are very low, whereas societies with a “buy‑now‑pay‑later” ethos may borrow heavily despite high rates.

3. Definition of “rate of interest” (AO1)

The rate of interest is the price of money. It is the cost of borrowing for those who take out a loan and the reward for saving for those who deposit money, lend or buy interest‑bearing assets. In formula form the (nominal) rate is usually written as i % per period.

4. How a change in the interest rate influences the three household choices

1. Spending (current consumption)

   • Higher rates → borrowing becomes more expensive and the opportunity cost of holding cash rises → current spending falls.
   • Lower rates → credit is cheaper and the opportunity cost of cash falls → current spending rises.

2. Saving

   • Higher rates → a larger return on deposits or bonds → saving increases.
   • Lower rates → a smaller return → saving decreases (or households look for alternative assets).

3. Borrowing (demand for loans or mortgages)

   • Higher rates → higher interest repayments → borrowing falls.
   • Lower rates → cheaper credit → borrowing rises.

5. Real vs. nominal interest rate

Households care about the purchasing power of the money they will receive (or repay) in the future. Therefore the real interest rate is the relevant figure:

\[

r = i - \pi^{e}

\]

where i = nominal interest rate, \pi^{e} = expected inflation over the same period, and r = real interest rate.

• Why it matters: A nominal rate of 5 % with expected inflation of 2 % gives a real return of only 3 %. Decisions to save or borrow are based on that 3 %.
• Forming expectations: Households use recent price trends, central‑bank forecasts and personal experience to form \(\pi^{e}\).

Worked conversion example (nominal → real)

1. Given: nominal rate \(i = 5\%\), expected inflation \(\pi^{e}=2\%\).
2. Apply the formula: \(r = 5\% - 2\% = 3\%\).
3. Interpretation: The household’s real reward for saving is 3 % and the real cost of borrowing is also 3 %.

6. Diagram – Inter‑temporal budget constraint (AO2)

The diagram shows two inter‑temporal budget lines for the same household:

• Horizontal axis: current‑period consumption (\(C_{1}\)).
• Vertical axis: future‑period consumption (\(C_{2}\)).
• Slope of each line = \(-\,(1+r)\). A higher real rate makes future consumption relatively cheaper, rotating the line clockwise (steeper).

Current‑period consumption (C₁)

Future‑period consumption (C₂)

r = 2 % (flatter)

r = 8 % (steeper)

O

Caption: Inter‑temporal budget lines for a household when the real interest rate is low (2 %, flatter line) and when it is high (8 %, steeper line). The steeper line shows that a given amount of current consumption can be exchanged for a larger amount of future consumption, encouraging the household to save more today.

7. Numeracy – Step‑by‑step calculations

Example 1 – Saving decision (future value)

A household saves £1 000 for one year at a nominal rate of 5 % while expected inflation is 2 %.

1. Calculate the real interest rate: \(r = 5\% - 2\% = 3\%\).
2. Future nominal value (FV):
   

   \[

   FV = 1\,000 \times (1 + 0.05) = £1\,050

   \]

3. Convert to real purchasing power by removing expected inflation:
   

   \[

   \text{Real value} = \frac{FV}{1 + \pi^{e}} = \frac{1\,050}{1 + 0.02} \approx £1\,029.41

   \]

4. Real gain = £29.41, i.e. a 2.9 % increase in real terms. The household compares this gain with the utility of spending the £1 000 today.

Example 2 – Borrowing decision (present value of a mortgage)

A family is offered a 5‑year mortgage of £20 000 with annual repayments of £4 600. The nominal interest rate is 6 % and expected inflation is 2 %.

1. Real interest rate: \(r = 6\% - 2\% = 4\%\).
2. Present value (PV) of the repayment stream using the real rate:
   

   \[

   PV = \sum_{t=1}^{5} \frac{4\,600}{(1 + 0.04)^{t}}

   \]

3. Calculate each term:

   • \(t=1:\; \frac{4\,600}{1.04}=4\,423.08\)
   • \(t=2:\; \frac{4\,600}{1.04^{2}}=4\,251.04\)
   • \(t=3:\; \frac{4\,600}{1.04^{3}}=4\,084.27\)
   • \(t=4:\; \frac{4\,600}{1.04^{4}}=3\,922.57\)
   • \(t=5:\; \frac{4\,600}{1.04^{5}}=3\,765.75\)

   Adding them gives \(PV \approx £20\,447\) (rounded). Because the loan amount is £20 000, the real cost of the loan is slightly higher than the amount borrowed.

4. Interpretation: If the household expects the real rate to fall to 2 % later, the PV would rise above £20 000, making the loan more expensive in real terms and possibly deterring borrowing.

8. Summary table – Effects of a change in the interest rate

9. Evaluation – Why the interest‑rate effect is not the whole story

When answering exam questions, use a clear mini‑framework and illustrate it with a concrete situation.

1. Interaction with the other four influences – A rise in rates may be offset by a rise in disposable income or a surge in consumer confidence, leaving net spending unchanged.
2. Expectations of future rate movements – If households anticipate that rates will fall soon, they may postpone borrowing even when current rates are relatively low.
3. Access to credit – In a credit‑constrained economy (tight lending standards), a low nominal rate may not translate into higher borrowing.
4. Behavioural and cultural factors – Some societies have a strong aversion to debt; others encourage “buy‑now‑pay‑later” behaviour, moderating the interest‑rate effect.
5. Time‑horizon and age – Young households with long horizons are more responsive to rate changes than retirees, who are mainly concerned with preserving capital.

Illustration: During a recession, the central bank cuts the nominal rate from 6 % to 2 %. Expected inflation falls from 3 % to 1 %, so the real rate drops from 3 % to 1 %. The lower real rate encourages borrowing, but at the same time consumer confidence plummets and many households experience a fall in income. The combined effect may be a modest rise in borrowing but little change in current spending, showing that the interest‑rate influence must be evaluated alongside the other four factors.

10. Key points to remember (AO1)

• The rate of interest is the price of money – it is both the cost of borrowing and the reward for saving.
• Higher rates generally lead to ↓ spending, ↑ saving and ↓ borrowing; lower rates have the opposite effect.
• Households make decisions on the real interest rate: \(r = i - \pi^{e}\).
• The five influences (income, interest rate, confidence, age, culture) operate together; the net effect on behaviour depends on how they interact.
• Use the inter‑temporal budget‑line diagram to show how a change in the real rate rotates the budget constraint and alters the trade‑off between current and future consumption.
• In exam answers, always state the relevant formulae, carry out the required calculations step‑by‑step, and evaluate the result by referring to the other four influences.