20. An investment pays you an annual stated rate (nominal rate) of 9 percent interest, compounded annually. A second investment of equal risk pays interest.compounded quarterly. What nominal annual rate of interest would you have to receive on the second investment in order to make you indifferent between the two investments? 21. You have a conventional, $175.000, fixed-rate 30-year mortgage with a 9 percent nominal rate and monthly payments/compounding. What will be the remaining balance on your mortgage after 6 years (that is, immediately after the 72nd payment)? 165)918. 31859 22. You took out a 30-year mortgage for $150,000 exactly 5 years ago (ie, you just made your 60th payment). The loan had a nominal annual interest rate of 6% with monthly payments. Assuming all of your payments have been made on-time, how much of your next payment will go towards interest? 23. You can purchase an annuity that pays $1000 per year for 5 years. The first payment will be received exactly one year from today. If the interest rate is 8%, compounded quarterly, what is the most you would be willing to pay for the annuity (rounded to the next Sy? 24. John starts to save money for his retirement. Beginning today he will deposit the same fixed amount each year for the next 20 years into a retirement savings account (ie, he will make 20 equal annual deposits). Starting one year after making his final deposit, he will withdraw S100,000 annually for each of the following 10 years (ie, he will make 10 withdrawals in all). Assume that the retirement fund carns 6% annually over both the period that he is depositing money and the period he makes withdrawals. In order for John to have sufficient funds in his account to fund his retirement, how much should he deposit annually (rounded to the nearest dollar)? 25. A quarterly compounded investment of $10,000 is expected to grow to $20,000 in 7 years. What is the underlying effective annual interest rate? 26. Boldana Corp. is considering a project that has an initial cost today of $20,000. The project has a two-year life with cash inflows of $13.000 a year. Should Boldana decide to wait one year to commence this project, the initial cost will increase by 5% and the cash inflows will increase to $15,000 a year. What is today's value of the option to wait if the applicable discount rate is 129 (rounded to the nearest S)? 27. Mr. X starts to save money for his tuition payments needed for a reputed MBA program he wishes to begin in 5 years. Beginning today he will deposit $5000 each year into a MBA tuition account. The last payment will be made 5 years from today (i.e., he will make 6 equal annual deposits). Assume that the MBA tuition account earns 4% annually over the period that he is depositing money. The amount he will have in his account 5 years from today, right after his last payment is closest to: 28. Assume that Claudia started a paper route on January 1, 1970. Since that day, at the end of every three (3) months (first deposit made on April 1, 1970), she deposited $500.00 into a savings account, which paid her interest of 4 percent annually but with quarterly compounding. On January 1, 1980, she took the balance in her savings account and transferred it to an account that paid 11.5% pa. Assuming that Claudia did not deposit any additional money into the account after the transfer, how much did she have in her account on January 1, 20147 21 12 29. On the day that his first child was born, Ezio Auditore de Firenze deposited $3,000 into an investment account. The only purpose for the account was to nay for his son's first year of college tuition. Assume that his son, Flavia, started college on his 18 birthday and his first year tuition payment had to be made that day. The amount needed on that day was $26.000. If that was indeed the amount of money in the account on Flavia's 18th birthday, what annual rate of return did Ezio earn on his investment account? 12.8
