$7.$ Sam just took out a $$15,000,$ four year loan to purchase a car. If the interest rate on the loan is $8\%$ compounded monthly, what will Sam's monthly car payment be$?$

A$.$$ $366\mathrm{.}19($Correct Answer$)$

B$.$$$425\mathrm{.}81$

C$.$$$377\mathrm{.}40$

D$.$$$230\mathrm{.}60$

E$.$$$269\mathrm{.}54$

$8.$ A perpetuity will pay $$1,000$ per year, starting $5$ years from today. What is the present value of this perpetuity, given the relevent interest rate is $4\%?$

A$.$ $$25,000$

B$.$ $$20,582$

C$.$ $$34,604$

D$.$ $$37,558$

E$.$ $$21,370($Correct Answer$)$

$9.$ You deposit $$160$ today and another $$200$ three years from today into an investment account. The investment pays $2\%$ compounded annually for the first two years, and $4\%$ annually thereafter. What is the combined future value five years from today?

A$.$ $$385\mathrm{.}51$

B$.$$$412\mathrm{.}87$

C$.$ $$391\mathrm{.}62$

D$.$$$403\mathrm{.}57($Correct Answer$)$

E$.$ $$433\mathrm{.}57$

$10.$ Your daughter is born today and you want here to be a millionare by the time she is $35$ years old. You open an investment account that promises to pay $12\%$ per year. How much must you deposit each year, starting on her $1$st birthday and ending on her $35$th birthday, so your daughter will have $$1,000,000$ by her $35$th birthday?

A$.$ $$5,777$

B$.$ $$3,455$

C$.$ $$9,450$

D$.$ $$2,317($Correct Answer$)$

E$.$ None of these

$10.$ You navigate a $7-$ year loan of $$70,000$ to SHSU Inc. To repay you, SHSU has agreed to pay $$4,000$ at the end of Year $1,$ $$8,000$ at the end of yer $2,$ $$12,000$ at the end of year $3,$ $$16,000$ at the end of year $4,$ plus a fixed but unspecified cash flow $"$x$",$ at the end of each year from year $5$ through year $7.$ You reguard $9\%$ as an appropriate rate of return on this low risk loan. What cash flow must the investment provide at the end of each of the final $3$ years to satisfy your return requirement? $($ i$.$e What is $"$X$"?)$

A$.$ $$27,678\mathrm{.}10$

B$.$$$25,567\mathrm{.}10$

C$.$$$19,958\mathrm{.}10$

D$.$$$21,746\mathrm{.}10($Correct Answer$)$

E$.$$$23,114\mathrm{.}10$

Please provide step by step solution for each problem. As well as provide instruction on how to solve manually on a financial calculator.