Simon recently received a credit card with a $21\%$ nominal

interest rate. With the card, he purchased an Apple iPhone $11$ for

$$670.$ The minimum payment on the card is only $$20$ per month.If Simon makes the minimum monthly payment and makes no other

charges, how many months will it be before he pays off the card? Do

not round intermediate calculations. Round your answer to the

nearest whole number.$$month$($s$)$If Simon makes monthly payments of $$70,$ how many months will it

be before he pays off the debt? Do not round intermediate

calculations. Round your answer to the nearest whole number.$$month$($s$)$How much more in total payments will Simon make under the

$$20-$a$-$month plan than under the $$70-$a$-$month plan? Do not round

intermediate calculations. Round your answer to the nearest

cent.$$$It is now December $31,2020($t $=0),$ and a jury just found in

favor of a woman who sued the city for injuries sustained in a

January $2019$ accident. She requested recovery of lost wages plus

$$450,000$ for pain and suffering plus $$90,000$ for legal expenses.

Her doctor testified that she has been unable to work since the

accident and that she will not be able to work in the future. She

is now $62,$ and the jury decided that she would have worked for

another $3$ years. She was scheduled to have earned $$44,000$ in $2019.$

$($To simplify this problem, assume that the entire annual salary

amount would have been received on December $31,2019.)$ Her employer

testified that she probably would have received raises of $3\%$ per

year. The actual payment for the jury award will be made on

December $31,2021.$ The judge stipulated that all dollar amounts are

to be adjusted to a present value basis on December $31,2021,$ using

a $5\%$ annual interest rate and using compound, not simple, interest.

Furthermore, he stipulated that the pain and suffering and legal

expenses should be based on a December $31,2020,$ date. How large a

check must the city write on December $31,2021?$ Do not round

intermediate calculations. Round your answer to the nearest

dollar.$$Your father is $50$ years old and will retire in $10$ years. He

expects to live for $25$ years after he retires, until he is $85.$ He

wants a fixed retirement income that has the same purchasing power

at the time he retires as $$40,000$ has today. $($The real value of his

retirement income will decline annually after he retires.$)$

His$$retirement income will begin the day he

retires,$10$ years from today, at which time he will

receive $24$ additional annual payments. Annual inflation is expected

to be $6\%.$ He currently has $$185,000$ saved, and he expects to earn

$8\%$ annually on his savings. How much must he save during each of

the next $10$ years $($end$-$of$-$year deposits$)$ to meet his retirement

goal? Do not round intermediate calculations. Round your answer to

the nearest dollar.$$$A father is now planning a savings program to put his daughter

through college. She is $13,$ plans to enroll at the university in $5$

years, and she should graduate $4$ years later. Currently, the annual

cost $($for everything $-$ food, clothing, tuition, books,

transportation, and so forth$)$ is $$20,000,$ but these costs are

expected to increase by $5\%$ annually. The college requires total

payment at the start of the year. She now has $$8,000$ in a college

savings account that pays $6\%$ annually. Her father will make six

equal annual deposits into her account; the first deposit today and

sixth on the day she starts college. How large must each of the six

payments be$?($Hint: Calculate the cost $($inflated at $5\%)$ for each

year of college and find the total present value of those costs,

discounted at $6\%,$ as of the day she enters college. Then find the

compounded value of her initial $$8,000$ on that same day. The

difference between the PV of costs and the amount that would be in

the savings account must be made up by the father's deposits, so

find the six equal payments that will compound to the required

amount.$)$ Do not round intermediate calculations. Round your answer

to the nearest dollar.$$Quantitative Problem:$$You need $$20,000$ to

purchase a used car. Your wealthy uncle is willing to lend you the

money as an amortized loan. He would like you to make annual

payments for $5$ years, with the first payment to be made one year

from today. He requires a $7\%$ annual return.$$$Interest: $$$Principal repayment: $$$Quantitative Problem $1$:$$You plan to

deposit $$1,500$ per year for $6$ years into a money market account

with an annual return of $3\%.$ You plan to make your first deposit

one year from today.$$$$$$Quantitative Problem $2$:$$You and your wife

are making plans for retirement. You plan on living $30$ years after

you retire and would like to have $$100,000$ annually on which to

live. Your first withdrawal will be made one year after you retire

and you anticipate that your retirement account will earn $12\%$

annually.$$$$$$Quantitative Problem:$$Bank $1$ lends funds

at a nominal rate of $8\%$ with payments to be made semiannually. Bank

$2$ requires payments to be made quarterly. If Bank $2$ would like to

charge the same effective annual rate as Bank $1,$ what nominal

interest rate will they charge their customers? Do not round

intermediate calculations. Round your answer to three decimal

places.$$Quantitative Problem $1$:$$You deposit $$2,000$

into an account that pays $7\%$ per year. Your plan is to withdraw

this amount at the end of $5$ years to use for a down payment on a

new car. How much will you be able to withdraw at the end of $5$

years? Do not round intermediate calculations. Round your answer to

the nearest cent.$$$Quantitative Problem $2$:$$Today$,$ you invest

a lump sum amount in an equity fund that provides an $12\%$ annual

return. You would like to have $$10,300$ in $6$ years to help with a

down payment for a home. How much do you need to deposit today to

reach your $$10,300$ goal? Do not round intermediate calculations.

Round your answer to the nearest cent.$$$Quantitative Problem:$$You own a security

that provides an annual dividend of $$195$ forever. The security$$s

annual return is $4\%.$ What is the present value of this security?

Round your answer to the nearest cent.$$$Quantitative Problem:$$You own a security

with the cash flows shown below.If you require an annual return of $12\%,$ what is the present

value of this cash flow stream? Do not round intermediate

calculations. Round your answer to the nearest cent.$$\%$