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You plan to deposit $400 in a bank account now and $300 at the end of the year. If the account earns 4% interest per year, what will be the balance in the account right after you make the second deposit? You have a loan outstanding. It requires making five annual payments of $9,000 each at the end of the next five years. Your bank has offered to allow you to skip making the next four payments in lieu of making one large payment at the end of the loan's term in five years. If the interest rate on the loan is 5%, what final payment will the bank require you to make so that it is indifferent to the two forms of payment? You want to endow a scholarship that will pay $8,000 per year forever, starting one year from now. If the school's endowment discount rate is 4%, what amount must you donate to endow the scholarship? Assume that your parents wanted to have $170,000 saved for college by your 18 th birthday and they started saving on your first birthday. They saved the same amount each year on your birthday and earned 8.5% per year on their investments. a. How much would they have to save each year to reach their goal? b. If they think you will take five years instead of four to graduate and decide to have $210,000 saved just in case, how much would they have to save each year to reach their new goal? A rich relative has bequeathed you a growing perpetuity. The first payment will occur in a year and will be $5,000. Each year after that, you will receive a payment on the anniversary of the last payment that is 2% larger than the last payment. This pattern of payments will go on forever. Assume that the interest rate is 16% per year. a. What is today's value of the bequest? b. What is the value of the bequest immediately after the first payment is made? You work for a pharmaceutical company that has developed a new drug. The patent on the drug will last 17 years. You expect that the drug's profits will be $1 million in its first year and that this amount will grow at a rate of 5% per year for the next 17 years. Once the patent expires value of the new drug if the interest rate is 11% per year? You have an investment account that started with $4,00010 years ago and which now has grown to $12,000. a. What annual rate of return have you earned (you have made no additional contributions to the account)? b. If the savings bond earns 16% per year from now on, what will the account's value be 10 years from now? You are thinking of purchasing a house. The house costs $250,000. You have $36,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offering a 30 -year mortgage that requires annual payments and has an interest rate of 10% per year. What will be your annual payment if you sign this mortgage? A local bank is running the following advertisement in the newspaper: "For just $1,000 we will pay you $100 forever!" The fine print in the ad says that for a $1,000 deposit, the bank will pay $100 every year in perpetuity, starting one year after the deposit is made. What interest rate is the bank advertising (what is the rate of return of this investment)