Sources of finance and borrowing

You want a bicycle costing $240\ \text{€}$. Explain the difference between paying for it with savings (you have been saving $20\ \text{€}$ for months) and paying for it with an "instant" loan offered by the shop. What does each option gain and risk? In which scenarios would each option make sense?

Explain the difference between own funding (savings, members' contributions) and external funding (loans, which must be repaid with interest). Classify: the $40\ \text{€}$ each member puts in, a loan from the PTA, last year's reinvested profits and a bank microloan.

Name four sources of funding for the school project (the team's savings, a loan from the PTA, pre-selling vouchers, crowdfunding) and write one advantage and one drawback of each in one sentence.

Interest is the cost of borrowing money. Calculate the simple interest on a deposit of $100\ \text{€}$ at $5\ \%$ per year for one year: how many euros does it generate and how much money do you end up with? What if you leave it for two years at simple interest?

Calculate the simple interest of these loans with $I = C \cdot r \cdot t$: (a) $200\ \text{€}$ at $5\ \%$ a year for $1$ year; (b) $200\ \text{€}$ at $5\ \%$ a year for $3$ years; (c) $500\ \text{€}$ at $4\ \%$ a year for $2$ years. State in each case how much is repaid in total.

Your grandmother lends you $500\ \text{€}$ for your school project and (jokingly) charges you simple interest of $4\ \%$ per year. Calculate: (a) the interest for each year; (b) the amount you would repay her if you take $3$ years to pay her back; (c) the interest you would pay if you take only $6$ months. Remember that with simple interest, $I = C \cdot r \cdot t$.

The figure compares two ways to grow $1.000\ \text{€}$ at $10\ \%$ per year over $3$ years: with simple interest (blue line, the same amount is added each time) and with compound interest (green curve, interest also earns interest).

1. a) Read from the graph how much money there is after $3$ years with each method and calculate the difference.
2. b) Explain in your own words why the green curve pulls further and further away from the blue line.

You deposit $1.000\ \text{€}$ at $5\ \%$ per year with compound interest. Calculate the principal at the end of the first year and, using that result, the principal at the end of the second year (round to the nearest cent). Compare this with simple interest over two years and explain where the difference comes from.

You deposit $800\ \text{€}$ in an account at $3\ \%$ a year with compound interest.

1. a) Calculate the capital after $1$ year and, from that result, after $2$ years (round to the nearest cent).
2. b) Calculate the same with simple interest and explain where the difference comes from and why it would grow over the years.

Two loan adverts for a $900\ \text{€}$ computer: shop A, $12$ instalments of $82\ \text{€}$; shop B, $18$ instalments of $56\ \text{€}$.

1. a) Calculate the total paid and the cost of the financing in each shop.
2. b) Explain why the lowest instalment (shop B) works out more expensive in total and what practical rule follows about the length of consumer loans.

Lucas, aged $19$, earns a net salary of $950\ \text{€}$ per month on a temporary contract. He lives with his family and contributes $200\ \text{€}$ towards household expenses; in addition, he pays $45\ \text{€}$ per month to finance his computer. He wants to buy a second-hand motorbike, and the dealership offers him two options:

• Option A: An instalment of $190\ \text{€}$/month for $24$ months. The sales representative reassures him: "Your total debt will be $235\ \text{€}$ per month, which is $24,7\ \%$ of your salary. The golden rule says that as long as you do not exceed $30\ \%$, you are in a completely safe zone."

• Option B: A reduced instalment of $120\ \text{€}$/month for $48$ months with a final payment of $800\ \text{€}$.

Insurance, fuel, and maintenance for the motorbike will entail an additional fixed cost of $110\ \text{€}$ per month.

1. a) Refute the sales representative's argument regarding Option A: calculate the real financial burden (total instalments plus expenses associated with the vehicle) relative to his disposable income after contributing at home, and predict what would happen to his solvency if his working hours were reduced by $20\ \%$.
2. b) Evaluate Option B: calculate the total cost of both options and justify which alternative Lucas should adopt to avoid over-indebtedness, taking into account the duration of his contract and his prior savings options.

In a WhatsApp group, you are invited to join the "Solidarity Savings Wheel": you contribute $20\ \text{€}$ to enter and must recruit $2$ people who contribute another $20\ \text{€}$ each. The administrator claims that when the wheel moves up a level, you will receive $190\ \text{€}$ "clear and guaranteed". Your cousin shows you a screenshot of his account to prove to you that he has already been paid.

1. a) Model the scheme mathematically: if each participant must contribute $20\ \text{€}$ and recruit $2$ new members, calculate how many new members are needed in rounds $1$, $2$, $3$, $5$, and $10$ to pay the previous levels. Demonstrate what percentage of the total people entering the system will inevitably lose their money when it is no longer possible to recruit more people.
2. b) Based on the principles of profitability, risk, and value creation in the real economy, refute your cousin's screenshot argument: justify why early participants getting paid does not prove the system's viability, and explain how to distinguish this mechanism from an investment or a legitimate savings fund.