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Matemáticas Financieras
Session 5
Classic Capitalization Laws
Problem 1 Calculate the future value of the following dated payments using an annual 6% nominal APR rate with annual compounding
- 1.000¿ today, capitalized 6 months from today
- 1.500¿ today, capitalized 3 years from today
- 500¿ 2 moths from today, capitalized to 8 months from today
- 2000¿ next year, capitalized to 6 years from today
- 500¿ today and 500¿ in 6 months, capitalized to 5 years from today
Problem 2 Redo the previous exercise using monthly compounding with the same 6% annual interest rate (nominal APR)
Problem 3 Compute the present value (value today) of the following dated payments, using an annual 12% eective APR and annual compounding
- 1.000¿ one month from today
- 1.500¿ in 3 years' time
- 500¿ in 3 months' time
- 2000¿ next year
- 500¿ in 6 months' time and 500¿ in 12 months' time
Problem 4 Repeat the previous exercise using monthly compounding and the same 12% eective APR
Problem 5 You've won a prize from a breakfast cereal company. You can choose to receive the prize in one of the following ways:
100,000.00¿ today
180,000.00¿ in ve years' time
29,500.00¿ per year for ve years
18,000.00¿ every six months for ve years
Which is the most valuable price is your bank oers you a money market account where you can save at a 3% nominal APR with interest paid every six months?
Problem 6 Jordi and Elena are saving to buy a 4x4 in ve years' time. The car's price will be 40,000.00¿ and they can get a 5% eective APR on their savings. What constant yearly amount do they need to save for the next ve years in order to buy the car (in cash)?
Problem 7 Your company has debt with a value (today) of 100,000.00¿. The rm's current liquidity problems force you to cancel the debt so you have to negotiate with the bank. They oer to re nance it by converting it into a debt with three equal annual installments. The rst installment will be in one year's time. The bank demands a 5% eective APR. Determine the size of the installments.
Problem 8 You have two savings accounts in dierent banks. One pays interests every month and the other every three months. The rst bank will give you a payment of 10¿ this month, while the second bank will pay you 60¿ this quarter. The nominal APR on both accounts is the same and equal to 6%. Determine how much money you have in each of the two accounts.
Problem 9 An investor is oered two dierent securities in which to invest. The rst oers interest payments of 1.5% every six months, while the second 1.5% every three months. Which of the two oers you a higher eective APR? What would the half-yearly eective interest rate on the rst security need to be in order for the eective APR on both securities to be the same?
Problem 10 You hold a bill of payment of 15.000¿ from Elimpagao S.A which is due today. You receive a call from your bank manager informing you that the payment has not arrived. You call the nancial director of Elimpagao S.A., Mr. Longshot. Longshot tells you that he is running into a temporary liquidity problem but will have the money in three months' time. He oers to pay back the debt with a 12% nominal APR. How much money (cash) will you receive if you accept his proposal? (Don't forget to use simple capitalization)
Problem 11 You have a second bill of payment from Elimpagao S.A. for 15.000¿ which is due in 6 months' time. You need the money now to pay your workers' salaries this month so you go to a nancing company. They oer you a six month loan at an 8% nominal APR and accepts the bill of payment as collateral. What is the maximum amount of money you can borrow from the nancing company such that you can pay back the loan plus interest with the 15.000¿ you will be collecting from Elimpagao S.A.?
Problem 12 Your aunt has divorced and from the settlement, she has received 35.000¿ in a savings account that earns a 5% annual interest rate with annual compounding and a house. The house was bought with a loan that has a single payment due: 42.000¿ four years from today. The debt can be canceled today by paying 35.000¿ and your aunt asks you what should she do
What is her best option?
How would your analysis change if you take into account that your aunt has to pay taxes of 15% on the interest she receives from her savings?
Problem 13 Shark Investments Corp. oers you the following investment product: invest 1000¿ today and receive 1600¿ in eight years' time. What is the eective APR on this investment? What is the continuously compounded interest rate?
Problem 24 (EX 2014) A large store oers clients a 10% cash discount for cash payments in the electronics department. Clients can also possible pay their purchases in three equal monthly installments (the rst one at the end of one month) without any interest payments. You want to buy a computer with a price of 1500 euros and you have the money to pay in cash if you want to. What is the best option if the market interest rate is a 3% eective annual interest rate?
