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.

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.

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).

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).

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.

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.

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.

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 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.

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.