LO$230.$ Calculating Amnuities Due You want to buy a new sports car from Muscle Motors for $$65,500.$ The contract is in the form of a $60-$month annuity due at an APR of $4\mathrm{.}1$ percent. What will your monthly payment be$?$

LO$431.$ Calculating Interest Expense You receive a credit card application from Shady Banks Savings and Loan offering an introductory rate of $1\mathrm{.}25$ percent per year, compounded monthly for the first six months, increasing thereafter to $17\mathrm{.}8$ percent per year, compounded monthly. Assuming you transfer the $$9,000$ balance from your existing credit card and make no subsequent payments, how much interest will you owe at the end of the first year?

LO$432.$ Calculating the Number of Periods You are saving to buy a $$275,000$ house. There are two competing banks in your area, both offering certificates of deposit yielding $4\mathrm{.}8$ percent. How long will it take your initial $$90,000$ investment to reach the desired level at First Bank, which pays simple interest? How long at Second Bank, which compounds interest monthly?

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LO$433.$ Calculating Future Values You have an investment that will pay you $1\mathrm{.}21$ percent per month. How much will you have per dollar invested in one year? In two years?

LO$434.$ Calculating Annuity Interest Rates Although you may know William Shakespeare from his classic literature, what is not well$-$known is that he was an astute investor. In $1604,$ when he was $40$ and writing King Lear, Shakespeare grew worried about his eventual retirement. Afraid that he would become like King Lear in his retirement and beg hospitality from his children, he purchased grain "tithes," or shares in farm output, for $440$ pounds. The tithes paid him $60$ pounds per year for $31$ years. Even though he died at the age of $52,$ his children received the remaining payments. What interest rate did the Bard of Avon receive on this investment?

LO$135.$ Comparing Cash Flow Streams You've just joined the investment banking firm of Dewey, Cheatum, and Howe. They've offered you two different salary arrangements. You can have $$90,000$ per year for the next two years, or you can have $$77,000$ per year for the next two years, along with a $$20,000$ signing bonus today. The bonus is paid immediately and the salary is paid in equal amounts at the end of each month. If the interest rate is $7$ percent compounded monthly, which do you prefer?

LO$136.$ Calculating Present Value of Annuities Peter Lynchpin wants to sell you an investment contract that pays equal $$25,000$ amounts at the end of each year for the next $20$ years. If you require an effective annual return of $9$ percent on this investment, how much will you pay for the contract today?

LO$437.$ Calculating Rates of Return You're trying to choose between two different investments, both of which have up$-$front costs of $$25,000.$ Investment $G$ returns $$60,000$ in six years. Investment H returns $$92,000$ in nine years. Which of these investments has the higher return?

LO$138.$ Present Value and Interest Rates What is the relationship between the value of an annuity and the level of interest rates?

Suppose you just bought an annuity with $13$ annual payments of $$10,000$ per year at a discount rate of $10$ percent per year. What happens to the value of your investment if interest rates suddenly drop to $5$ percent? What if interest rates suddenly rise to $15$ percent?