Topic 1. Time value of money Exercise 1. You have just finished school and you need money to buy a motorcycle. Your rich grandmother will lend you the money if you agree to pay it back to her within four years and you offer to pay her the interest rate she would otherwise have received by putting her money in a savings account. Based on your income and living expenses, you think you can pay her $5,000 for one year and then $3,000 each year for the next three years. 1. If your grandmother was otherwise earning 5% a year on her savings, how much can you borrow from her? 2. Suppose your grandmother gives you money and you make your bank payments to her every year. How old will she be in four years? Exercise 2. Bob is 35 and he has decided it's time to seriously prepare for his retirement. At the end of each year until he is 65, he will put $10,000 into a retirement account. If the account earns 10% per year, how much will Bob have in the account at age 65? Exercise 3. Your firm plans to buy a cafe for $100,000. The bank offers you a loan for a period of 30 years with equal annual payments and an interest rate of 8% per year. The bank requires your firm to pay 20% of the purchase price as a down payment. What is the annual loan payment? Exercise 4. From renting a one-room apartment in Moscow, you plan to receive 384,000 rubles a year for 6 years. Then you are going to sell the apartment. According to your estimates, the cost of the apartment in 6 years will be 9,000,000 rubles. Getting these incomes is associated with a certain probability and risk, which analysts estimate at 10%. Determine the present value of your income stream if the flows come in at the end, beginning and middle of the year. Is it profitable for you to rent an apartment and sell it after 6 years, if the cost of this apartment on the market at the time of the assessment is 7,000,000 rubles. Exercise 5. The depositor deposited 1,000,000 rubles in a bank account. The Bank annually accrues 20% per annum, taking into account their capitalization. Simple interest is charged throughout the year. Determine how much the investor will receive after 5 years and sixty days. Exercise 6. How long will it take for the amount of 100,000 rubles. increased to 205,000 rubles at the rate of 20% per annum Exercise 7. The investor's investment horizon is 4 years. At the end of the first year he received 1 million rubles, the second - 2 million rubles, the third-2.5 million rubles, the fourth - 2.7 million rubles. and invested the amount of each payment at 15% per annum until the end of this four-year period. Determine the future value of the stream of payments
