Saving, investment and financial products

Name the three functions of money and classify these situations according to the function they illustrate: paying for a coffee with a coin, comparing the price of two mobile phones, and keeping banknotes in a piggy bank for a trip.

Distinguish between saving and investment, and classify the following decisions: putting money into a savings account, buying a new oven for a bakery, buying shares in a company, and keeping banknotes in a piggy bank. Which of them creates productive capacity?

You deposit $1.000\ \text{€}$ in an account paying simple interest of $4\ \%$ per year.

1. a) What interest do you receive after one year? And after two years?
2. b) What total amount do you have at the end of the second year?

The figure compares how $1.000\ \text{€}$ at $5\ \%$ per year evolves over ten years with simple interest and with compound interest. One of the lines (blue) and the other (orange) each correspond to one type of interest.

1. a) Which line (the blue one or the orange one) corresponds to each type of interest? Justify your answer.
2. b) Read from the graph, approximately, the accumulated difference at the end of the period and explain what causes it.

You deposit $1.000\ \text{€}$ at $5\ \%$ per year with compound interest for three years.

1. a) Calculate the balance at the end of each year, rounding to the nearest cent.
2. b) Explain why the interest in the third year is greater than in the first.

A financial advisor proposes two options to Lucía to generate returns on $10.000\ \text{€}$ that she will not need for the next $15$ years:

• Option A: A guaranteed product that pays the returns annually into her checking account at $4\ \%$ per year, money that Lucía does not reinvest but leaves idle at $0\ \%$.

• Option B: An accumulation fund that automatically reinvests the annual returns at that same rate of $4\ \%$ compounded annually.

Lucía states: "After $15$ years, I will have earned exactly the same profit from both products, $6.000\ \text{€}$, because the interest rate of $4\ \%$ and the term of $15$ years are identical."

1. a) Numerically demonstrate Lucía's mistake by calculating the final accumulated capital and the net profit obtained in each option after $15$ years. Explain the reason for the mathematical divergence between both results.
2. b) Assume that average inflation over that period is $2,5\ \%$ per year. Evaluate whether Lucía has preserved the real purchasing power of her initial $10.000\ \text{€}$ with each option. Based on your results, justify the practical relevance of reinvesting returns for a long-term saver against monetary erosion.

What is interest and why does someone who lends money charge it? Calculate the interest on lending $500\ \text{€}$ for one year at $3\ \%$ simple interest and explain what that payment compensates the lender for.

Explain the difference between a current account and a fixed-term deposit: how do they differ in availability of the money (liquidity) and in remuneration? What type of saving would you use each one for?

Three options for $5.000\ \text{€}$: a guaranteed deposit at $1\ \%$, a mixed fund with an expected return of $4\ \%$ but possible falls some years, and shares with an expectation of $7\ \%$ and high volatility.

1. a) Order the options from lowest to highest risk and explain the relationship between risk and expected return.
2. b) If the money is to pay for university in two years' time, which would you choose? Justify your answer using the time horizon.

A laptop costs $500\ \text{€}$ upfront, but the shop offers to pay for it in $12$ monthly instalments of $45\ \text{€}$.

1. a) Calculate how much you pay in total with the financing and how much the financing costs you.
2. b) What questions should you ask before agreeing to pay in instalments?

A couple takes out a mortgage of $120.000\ \text{€}$ for $25$ years to buy a flat.

1. a) Explain what the principal, the interest rate, and the term of this loan are.
2. b) If the rate rises from $3\ \%$ to $4\ \%$, explain without performing calculations what happens to the monthly instalment and to the total interest paid.

One bank offers a loan at a nominal rate of $5\ \%$ with no fees; another, at a nominal $4,5\ \%$ with a $1\ \%$ arrangement fee.

1. a) Explain what the APR is and why it is a better reference than the nominal rate for comparing both offers.
2. b) What other elements, besides the rate, should you compare before signing (term, instalment, tied products)?

Define in your own words the three elements of an insurance policy: the premium, the risk covered and the claim. Explain how it is possible for an insurer to pay for an $800\ \text{€}$ mobile phone in exchange for premiums of $8\ \text{€}$ a month: who really pays for that phone?

Mobile phone insurance costs $8\ \text{€}$ a month and home insurance costs $15\ \text{€}$ a month.

1. a) Explain what an insurance premium is and what risk each of these two transfers.
2. b) Reason why the insurer can charge such different premiums and what factors it will take into account when setting them.

A financial platform offers three investment alternatives to an individual:

• Asset Alpha: A $10$-year German sovereign bond with an annual coupon of $2,3\ \%$.

• Asset Beta: Shares of an emerging biotechnology company that will multiply its revenue if a medical patent is approved, but which is currently running losses.

• Asset Gamma: A corporate bond issued by a hotel company under bankruptcy proceedings (insolvency) offering an annual interest rate of $11,5\ \%$.

An inexperienced saver argues: "The smartest thing to do is to invest everything in Asset Gamma, since being fixed income, it contractually ensures that I receive more than four times what Germany offers, avoiding the uncertainty of the biotech company."

1. a) Refute the saver's claim by distinguishing between market risk and credit (or default) risk. Justify why the market sets such disparate interest rates between Asset Alpha and Asset Gamma.
2. b) Analyze the return-risk-liquidity trilemma across the three assets and explain, using the mechanism of capital supply and demand, why it is unfeasible for a product to simultaneously offer high returns, zero risk, and immediate liquidity.
3. c) If this saver needed full access to their money in exactly $18$ months to buy a vehicle, design and justify a suitable asset allocation strategy among these three assets.

Noa works as an engineer at a large publicly traded tech company and has accumulated a financial net worth of $50.000\ \text{€}$, invested entirely in her own company's shares. She justifies her stance by stating: “I know the company from the inside, I fully trust my colleagues, and that way I win twice over when the company thrives”.

1. a) Identify and classify the financial and asset risks Noa assumes by concentrating her savings and her source of earned income in the same company. Analyze the impact on her solvency if the company undergoes financial restructuring due to an industry crisis.
2. b) Refute Noa's statement by distinguishing between specific (diversifiable) risk and systematic (market) risk. Why should a well-informed investor never expect an extra return premium for taking on diversifiable risk?
3. c) Design a restructuring proposal for her $50.000\ \text{€}$ portfolio by applying the principle of diversification across asset classes, geographic areas, and economic sectors. Justify the percentages allocated to each category for a moderate risk profile, and explain how it reduces the correlation between her paycheck and her wealth.