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# 1-      ​(Loan amortization) On December​ 31, Beth Klemkosky bought a yacht for ​\$90 comma 000. She

paid ​\$12 comma 000 down and agreed to pay the balance in 7 equal annual installments that include both the principal and 13 percent interest on the declining balance. How big will the annual payments​ be?

2-      ​(Present value of annuity​ payments) The state​ lottery's million-dollar payout provides for ​\$1.1 million to be paid in 20 installments of ​\$55 comma 000 per payment. The first ​\$55 comma 000 payment is made​ immediately, and the 19 remaining ​\$55 comma 000 payments occur at the end of each of the next 19 years. If 9 percent is the discount​ rate, what is the present value of this stream of cash​ flows? If 18 percent is the discount​ rate, what is the present value of the cash​ flows?

3-     (Annuity payments) Lisa Simpson wants to have ​\$2 comma 000 comma 000 in 60 years by making equal annual​ end-of-the-year deposits into a​ tax-deferred account paying 9.25 percent annually. What must​ Lisa's annual deposit​ be?

4-      ​(Present value of a growing​ perpetuity) What is the present value of a perpetual stream of cash flows that pays ​\$3 comma 500 at the end of year one and the annual cash flows grow at a rate of 4​% per year​ indefinitely, if the appropriate discount rate is 14​%? What if the appropriate discount rate is 12​%?

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