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 $\$1\,000$ to your brother and he pays back $\$1\,040$ 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 $\$20\,000$ for a year, calculate the interest you receive.
2. b) If you borrow $\$100\,000$ 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.

Óscar's family took out a loan of $\$240\,000$ for a car at a variable interest rate. With the rate at $3\ \%$, they pay $\$7\,200$ 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 $\$40\,000$ 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 $\$2\,000\,000$ 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.

A family urgently needs to replace their broken boiler in the middle of winter. The quote amounts to $\$3,000$. They have exactly $\$3,000$ 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 $\$3,000$.

• Option B: Financing in $12$ monthly installments of $\$275$ 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.