Exercises: 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?

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?

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.

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.

Define what the TAE (annual equivalent rate) is in your own words: what it tells you about a loan and why it is better than looking only at the monthly instalment. An advert says 'only $25\ \text{€}$ a month': explain which two pieces of information you are missing to know how much you will pay in total.

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.

Explain what a guarantor is and why banks ask for one from young people or those with no track record. Take the case of your $19$-year-old cousin who applies for $3.000\ \text{€}$ for a course and the bank requires her mother to act as guarantor: what risk does the mother take on?

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.

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, $I = C \cdot r \cdot t$.

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.

The school cooperative needs $300\ \text{€}$ to start up the breakfast stall. Analyse four sources: the members' savings, a loan from the PTA (Parent-Teacher Association) to be repaid in $3$ months, an advance sale of breakfast vouchers to students, and reward-based crowdfunding. For each source, state: what it costs (money, commitment, work), what is risked, and what type of project it is best suited for.

The cooperative needs $400\ \text{€}$ for a badge-making machine. The PTA lends it the money at $3\ \%$ simple annual interest, to be repaid in $8$ months.

1. a) Calculate the total interest and what the cooperative will repay (careful: $t$ in years, $8$ months is $8/12$ of a year).
2. b) Compare with the option of waiting $8$ months, saving $50\ \text{€}$ a month from the profits: what is gained and what is lost with each option if the big fair is in $3$ months' time.

An online shop offers to finance a pair of $120\ \text{€}$ trainers in '$3$ interest-free instalments of $40\ \text{€}$', but charges $9\ \text{€}$ of 'handling fees' at the start.

1. a) Calculate how much you pay in total and what extra percentage that represents over the price.
2. b) Explain why 'interest-free' does not mean 'free' and which two checks you would make before accepting any financing on an online purchase.

The school vegetable garden team wants $250\ \text{€}$ for tools and is considering a pre-sale: selling $50$ basket vouchers of $5\ \text{€}$ each, redeemable in June for a basket of vegetables.

1. a) Calculate how much they raise if they sell all the vouchers and explain how this funding differs from a loan (what they give back and when).
2. b) Analyse the two main risks of the pre-sale (a bad harvest, more vouchers than baskets) and one measure for each.

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.

You need a laptop costing $600\ \text{€}$ for Sixth Form. Option A: save $60\ \text{€}$ per month for $10$ months and buy it afterwards. Option B: store loan: you take it home today and pay $12$ monthly instalments of $54\ \text{€}$.

1. a) Calculate how much you pay in total with each option and how much "getting it early" in Option B costs in euros and as a percentage of the price.
2. b) Reason in which situations paying this extra cost could be justified and what questions you should ask yourself before signing.

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.

Financial well-being starts with having an emergency fund for unexpected events (repairs, medical costs, loss of income), usually worth $3$ to $6$ months of expenses. Design an emergency fund plan for Alex, who earns $20\ \text{€}$ per week: estimate his essential weekly expenses, set how much he puts aside each week, and calculate how many weeks it will take to build an emergency fund worth two "months" of expenses. Explain what needs to happen for the plan to survive an expensive birthday or seasonal sales.

Your $18$-year-old brother wants a $2.400\ \text{€}$ motorbike. He works weekends and earns $260\ \text{€}$ a month. The shop offers to finance it over $24$ months with instalments of $115\ \text{€}$.

1. a) Calculate the total cost of the financing and what percentage of his monthly income the instalment represents (remember the $30\ \%$ benchmark as a prudent limit).
2. b) Design an alternative mixed plan (saving for $6$ months first and then financing only the rest over $12$ months), calculate how much he saves in interest with your own reasonable assumptions and explain what else improves besides the money.

The school cooperative has grown and needs $1.000\ \text{€}$ for an oven. Three options: a loan from the PTA at $4\ \%$ a year for $1$ year; a crowdfunding campaign with rewards (estimated cost of the rewards, $150\ \text{€}$); selling $200$ stakes of $5\ \text{€}$ entitling the holder to a free breakfast a month for the school year (estimated cost, $300\ \text{€}$ in breakfasts).

1. a) Calculate the cost of each option and order them from cheapest to dearest.
2. b) Explain what each option offers beyond the money (community commitment, publicity, the obligation to repay) and choose one, defending it in front of the members.

A viral video claims: "Banks don't need your money: they create loans out of thin air by typing numbers into a computer. Charging you $5\ \%$ or $25\ \%$ interest is pure usury because it costs them nothing to generate that money."

To respond with economic rigor, you have two real applications analyzed by a financial institution:

• Application 1: A local bakery requests $10.000\ \text{€}$ over $4$ years at $5\ \%$ per annum for an energy-efficient industrial oven, providing sound annual accounts and a guarantor.

• Application 2: An individual without a steady payroll requests a quick online loan of $1.000\ \text{€}$ to be repaid in $6$ months to go on holiday, at an APR of $24,5\ \%$ and without requiring documentation.

1. a) Refute the video's claim by explaining the technical relationship between customer deposits, the legal reserve ratio ($1\ \%$ in the eurozone), and bank money creation. Why can't a bank lend unlimited funds at zero cost?
2. b) Technically justify the enormous difference in interest rates between both applications by breaking down their components (opportunity cost, inflation, management costs, and default risk premium). Predict what would happen to the bank's balance sheet if it were legally required to apply the same $5\ \%$ to both profiles.

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.

Design your school cooperative's 'funding policy' for the next $3$ years: what percentage of each project is funded with accumulated profits, when taking out a microloan is allowed (maximum amount, maximum term, who approves it) and which sources are banned and why (quick loans, undocumented debts between members). Defend the two rules that would generate the most debate.