Exercises: Interest rates and the European Central Bank

The interest rate is the price of money: what it costs to borrow it and what is paid when you lend it.

1. a) Explain this statement with an everyday example: you lend $50\ \text{€}$ to your brother and he pays back $52\ \text{€}$ the following year. What was the interest and the interest rate?
2. b) State who "pays the price" and who "earns it" when a family takes out a mortgage and when a grandmother opens a savings deposit.

A bank pays $2\ \%$ per year on savings deposits and charges $6\ \%$ per year on its loans.

1. a) If you deposit $1.000\ \text{€}$ for a year, calculate the interest you receive.
2. b) If you borrow $5.000\ \text{€}$ for a motorbike and take a year to repay it, calculate the interest you pay.
3. c) Explain where the bank gets its profit from.

The figure shows the sequence reported in the newspapers every time the European Central Bank raises interest rates to curb inflation, but one link is covered up.

1. a) State the missing link: what households and businesses do when borrowing costs more.
2. b) Explain the full sequence in your own words, and state what the ECB would do with interest rates if the economy were stagnant and inflation-free.

The European Central Bank (ECB), based in Frankfurt, is the central bank of the euro countries.

1. a) Explain its main mission: keeping inflation stable, close to $2\ \%$ a year, and why it wants it neither much higher nor much lower.
2. b) Name two of its decisions that reach your home (the rate at which banks finance themselves, which drives mortgages and deposits) and explain why it should be independent of governments.

The Euribor is the rate at which European banks lend money to each other, and it serves as the reference for most variable-rate mortgages in Spain.

1. a) Explain how the instalment of a variable-rate mortgage is formed (Euribor plus a margin, reviewed every $6$ or $12$ months).
2. b) Argue what happens to families with a variable-rate mortgage when the ECB raises rates and the Euribor follows.

When taking out a mortgage you can choose a fixed rate (the same instalment for ever) or a variable one (it changes with the Euribor).

1. a) Explain what risk you take on with each one and what profile of family fits each option better (tight incomes that need certainty?, room to withstand rises?).
2. b) Explain why the variable one usually starts out cheaper (the bank charges less because you take on the risk of the rises).

In loan adverts you will see two sets of initials: TIN (nominal interest rate, just the interest) and TAE (annual equivalent rate, like the APR: interest plus fees and charges, as an annual percentage).

1. a) Explain why, to compare two loans, you must look at the TAE and not the TIN.
2. b) A loan advertises 'TIN $0\ \%$' but charges a $60\ \text{€}$ arrangement fee on $1.000\ \text{€}$ over one year: calculate its approximate real cost as a percentage and comment on the advert.

You leave $1.000\ \text{€}$ in a deposit at $3\ \%$ a year with simple interest (each year you are paid only on the initial $1.000\ \text{€}$).

1. a) Calculate the interest for one year.
2. b) Calculate how much you will have after three years.
3. c) Explain the difference with compound interest (where the interest also earns interest) and why savers like the compound one.

Óscar's family took out a loan of $12.000\ \text{€}$ for a car at a variable interest rate. With the rate at $3\ \%$, they pay $360\ \text{€}$ in interest per year.

1. a) Calculate how much they would pay if the rate rises to $5\ \%$ and by how much their monthly interest bill increases.
2. b) Explain two decisions the family could make to absorb this increase and why consumer spending cools down when rates rise across the country.

For your $2.000\ \text{€}$ in savings, bank A offers a deposit account at $1\ \%$ per year and bank B at $3\ \%$.

1. a) Calculate the interest you would earn in one year at each bank.
2. b) Besides the interest rate, name three things you would check before deciding (fees/charges, whether you can withdraw money early, that the bank is reliable and covered by the Deposit Guarantee Scheme, which protects up to $100.000\ \text{€}$ per customer).

When inflation surges, the European Central Bank (ECB) usually raises interest rates. Put these steps in order and explain the chain of events: (1) households and businesses take out fewer loans; (2) the ECB raises rates; (3) borrowing costs more; (4) consumption and investment fall; (5) prices stop rising as quickly. What would the ECB do in a crisis with high unemployment and stable prices? Reason your answer using the same chain in reverse.

Bruno's family has a variable-rate mortgage with $120.000\ \text{€}$ outstanding. Last year, with the rate at $2\ \%$, it paid around $2.400\ \text{€}$ in interest.

1. a) If at the review the rate rises to $4\ \%$, calculate the new annual interest and the approximate monthly rise.
2. b) Explain three decisions the family can take (cutting leisure, extending the term if the bank allows it, renegotiating to a fixed rate) and what effect each one has.

To pay for the car ($8.000\ \text{€}$ over one year), bank A offers a TIN of $5\ \%$ with no fees; bank B, a TIN of $4\ \%$ with an arrangement fee of $2\ \%$.

1. a) Calculate the total cost of each option (interest plus fee).
2. b) Explain why the lowest TIN is not always the cheapest loan and which percentage best sums up the real cost (the TAE).

Your $3.000\ \text{€}$ deposit pays you $1\ \%$ a year and inflation is $3\ \%$.

1. a) Calculate the interest you receive in one year.
2. b) Calculate how much your $3.030\ \text{€}$ is worth measured in 'today's euros' (it has lost $3\ \%$ of its buying power) and explain what the real interest rate is (the nominal one minus inflation) and why it is negative here.
3. c) Argue what savers do when deposits lose against inflation.

With the latest mortgage review, Noa's parents' instalment has gone from $620\ \text{€}$ to $750\ \text{€}$ a month.

1. a) Calculate the rise in euros over one year.
2. b) Analyse its effect on the family budget: which items they would cut first and why.
3. c) Explain how that same rise, repeated across thousands of families at once, cools the country's consumption and ends up curbing inflation.

You leave $1.000\ \text{€}$ at $5\ \%$ a year for two years.

1. a) With simple interest, calculate the total (each year yields $50\ \text{€}$).
2. b) With compound interest, calculate the total (in the second year, the $5\ \%$ applies to $1.050\ \text{€}$).
3. c) Explain why the difference grows so much over the years (the snowball effect) and what saving advice follows from it (start early, even if it's little).

A family urgently needs to replace their broken boiler in the middle of winter. The quote amounts to $3.000\ \text{€}$. They have exactly $3.000\ \text{€}$ in an interest-bearing account earning $2\ \%$ annually, which makes up their entire emergency fund. The installer offers them two payment options:

• Option A: Single upfront payment of $3.000\ \text{€}$.

• Option B: Financing in $12$ monthly installments of $275\ \text{€}$ per month.

1. a) Calculate the total financial cost of deferring payment with Option B and the opportunity cost in interest if they choose Option A.
2. b) Looking solely at the mathematical result, Option A seems the most advantageous. However, analyze why paying in cash may represent a serious financial imprudence for this family's stability.
3. c) Design an intermediate or adjusted financial decision proposal for the family that balances interest savings with protection against liquidity risk.

In an economy, two worrying macroeconomic figures are recorded simultaneously: the year-on-year inflation rate has risen to $8,5\ \%$ (well above the $2\ \%$ target) and the unemployment rate has climbed to $14\ \%$.

1. a) Trace in an orderly manner the complete transmission chain that would be triggered if the Central Bank decides to raise official interest rates: deduce step by step the effects on bank credit, household consumption, business investment, aggregate demand, the general price level, and employment.
2. b) Justify what dilemma the monetary authority faces in this stagflation scenario and what inevitable cost its decision will have regardless of which path it chooses.
3. c) Knowing that the primary mandate of the European Central Bank is to guarantee price stability, predict what decision it will make and argue what complementary measures (outside monetary policy) the State should implement to cushion the impact on the most vulnerable sectors.

A social media headline claims: "The interest rate hike approved by the Central Bank proves that monetary policy only seeks to enrich big banks at the expense of impoverishing all families."

1. a) Refute the claim that "all families lose": compare in detail the net effect of a rate hike on a young family indebted with an adjustable-rate mortgage versus a family of retirees with fixed-term savings, also considering the impact of curbing inflation on the purchasing power of both households.
2. b) Analyze the situation of financial institutions: explain why a high interest rate scenario does not always translate into higher bank profits in the medium term (consider the volume of new loans granted and the risk of default or delinquency).
3. c) Justify the real purpose pursued by the ECB when making money more expensive and draft a critical conclusion that qualifies the headline's statement based on the concept of the macroeconomic common good.

A household with a combined net income of $2.800\ \text{€}$ per month applies for a $150.000\ \text{€}$, $25$-year mortgage loan. Their bank presents them with two alternatives:

• Fixed-rate mortgage: nominal interest rate of $3,2\ \%$ (constant payment of $727\ \text{€}/\text{month}$ over the $25$ years).

• Adjustable-rate mortgage: Euribor $+ 0,8\ \%$. At the time of signing, the Euribor is at $1,2\ \%$ (initial rate of $2\ \%$, payment of $636\ \text{€}/\text{month}$), reviewable once a year.

1. a) The prudential banking recommendation establishes that debt service should not absorb more than $35\ \%$ of net household income (financial effort ratio / debt-to-income ratio). Calculate the initial effort ratio for both options and interpret whether they are affordable for the family.
2. b) Conduct a stress test for the adjustable-rate mortgage: calculate the effort ratio if the Euribor rises by three percentage points (up to $4,2\ \%$, which raises the monthly payment to about $878\ \text{€}$). What consequences would this have for the household budget?
3. c) Design a justified recommendation for this family, assessing the risk factor over a $25$-year horizon: argue under what economic or personal circumstances it would be advisable for them to bear the initial extra cost of the fixed payment, and under which ones to take on the uncertainty of the adjustable rate.

An electoral candidate advocates in their economic platform: "To eradicate unemployment and help families, we will demand that the Central Bank set interest rates permanently at $0\ \%$ and lend unlimited money at zero cost."

1. a) Justify the mechanism by which this proposal would aim to stimulate employment and economic growth in the very short term through consumption and investment.
2. b) Predict and reason at least two serious macroeconomic imbalances that would inevitably arise if money were kept artificially "free" on an ongoing basis (consider inflation, the formation of bubbles in real estate or financial assets, and the penalty on savings).
3. c) Refute the candidate's proposal by explaining why central banks are institutions independent from political power and what the danger is of subordinating monetary control to electoral calendars.

Following a severe financial crisis, the Central Bank cut official interest rates practically to $0\ \%$ and provided massive liquidity to credit institutions. Despite this, over the next two years the volume of credit granted to households and SMEs continued to fall, and private consumption failed to rebound.

1. a) Diagnose this economic phenomenon (liquidity trap / balance sheet recession): why does lowering the cost of money prove ineffective when households and businesses are carrying excessive debt or a high fear of losing their jobs?
2. b) Identify in which part of the monetary transmission mechanism the breakdown has occurred: is the failure due to banks not passing on liquidity out of risk aversion, or because creditworthy demand for loans has disappeared? Justify both viewpoints.
3. c) Once conventional monetary policy exhausts its room for maneuver (reaching the zero lower bound on interest rates), justify which other macroeconomic policy must take the lead to stimulate aggregate demand and through which specific instruments it should do so.

Compare the disparate impact produced by a rapid ECB rate hike (from $0,5\ \%$ to $4\ \%$) on two companies in the same city:

• Company 1: "Estructuras Norte", a metallurgical company that has just undertaken a modernization of its industrial warehouses using adjustable-rate loans, and whose clients purchase industrial machinery through financing.

• Company 2: "Lácteos Valledulce", a cooperative producing basic daily consumer goods that has no external debt and holds accumulated cash reserves deposited in the bank.

1. a) Predict and contrast with reasoning how the ECB's decision will affect financial costs, product demand, and hiring decisions in each of the two companies.
2. b) Explain the ethical and macroeconomic dilemma: why does the Central Bank adopt a policy that it knows will harm production and employment in companies like "Estructuras Norte"?
3. c) Argue why, from the ECB's perspective, allowing inflation to become entrenched at high levels in the long run is considered a more damaging and regressive economic and social harm than the temporary slowdown in activity caused by the rate hike.

A family has $25.000\ \text{€}$ in a checking account and an outstanding variable-rate mortgage loan of $100.000\ \text{€}$. Analyze two different macroeconomic contexts:

• Context 1 (expansionary policy): Official interest rates and Euribor at $0,5\ \%$. The mortgage interest rate is $1,3\ \%$. Bank deposits yield a gross annual $0,1\ \%$.

• Context 2 (contractionary policy): Official interest rates and Euribor at $4\ \%$. The mortgage interest rate rises to $4,8\ \%$. Bank time deposits guarantee a gross annual $3,2\ \%$.

1. a) Calculate the annual mortgage interest expense and the gross annual income generated by the savings in the deposit for each of the two contexts.
2. b) In Context 2, the family considers using their $25.000\ \text{€}$ to pay off part of the mortgage debt early. Justify numerically why paying off the debt is more profitable for them than opening the bank deposit at $3,2\ \%$.
3. c) Design a prudent financial plan for the family in Context 2: why would it not be advisable for them to use the entire $25.000\ \text{€}$ to pay off the mortgage, even though the numbers from the previous section recommend it? Propose a justified split between early repayment and an emergency liquidity fund.