Payments with periodic rates.$$Denise has her heart set on being a millionaire. What payment does Denise need to make at the end of each six months over the coming $40$ years at $9\%$ APR to reach her retirement goal of $$$$1\mathrm{.}2$million$?$

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Part $1$

What semiannually payment does Denise need to make to reach her retirement$$ goal?

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enter your response here$($Round to the nearest$$ cent.$)$

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Present value with periodic rates.$$Sam$$ Hinds, a local$$ dentist, is going to remodel the dental reception area and add two new workstations. He has contacted$$ A$-$Dec, and the new equipment and cabinetry will cost $$$$16$ comma $000.$ The purchase will be financed with an interest rate of $10\%$ loan over $7$ years. What will Sam have to pay for this equipment if the loan calls for semiannual payments $(2$ per$$ year$)$ and monthly payments $(12$ per$$ year$)?$ Compare the annual cash outflows of the two payments. Why does the monthly payment plan have less total cash outflow each$$ year?

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Part $1$

What will Sam have to pay per period if the loan calls for semiannual payments $(2$ per$$ year$)?$

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$($Round to the nearest$$ cent.$)$

Future value with periodic rates.$$Matt Johnson delivers newspapers and is putting away $$$$16$ at the end of each month from his paper route collections. Matt is $8$ years old and will use the money when he goes to college in $10$ years. What will be the value of$$ Matt's account in $10$ years with his monthly payments if he is earning $4\%($APR$),10\mathrm{.}5\%($APR$),$ or $14\%($APR$)?$

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Part $1$

What will be the value of$$ Matt's account in $10$ years with his monthly payments if he is earning $4\%($APR$)?$

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$($Round to the nearest$$ cent.$)$