Complete all the questions below. Show the necessary steps in deriving your final answers.

If you deposit $$2,000$ in a bank account that pays $6\%$ interest annually, how much will be in your account after $5$ years?

What is the present value of a security that will pay $$29,000$ in $20$ years if securities of equal risk pay $5\%$ annually?

Your parents will retire in $19$ years. They currently have $$350,000$ saved, and they think they will need $$800,000$ at retirement. What annual interest rate must they earm to reach their goal, assuming they don't save any additional funds?

If you deposit money today in an account that pays $4\%$ annual interest, how long will it take to double your money?

You have $$33,556\mathrm{.}25$ in a brokerage account, and you plan to deposit an additional $$5,000$ at the end of every future year until your account totals $$220,000.$ You expect to carn $12\%$ annually on the account. How many years will it take to reach your goal?

You want to buy a car, and a local bank will lend you $$40,000.$ The loan will be fully amortized over $5$ years $(60$ months$),$ and the nominal interest rate will be $8\%$ with interest paid monthly. What will be the monthly loan payment? What will be the loan's EAR?

Starting next year, you will need $$5,000$ annually for $4$ years to complete your education. $($One year from today you will withdraw the first $$5,000.)$ Your uncle deposits an amount today in a bank paying $6\%$ annual interest, which will provide the needed $$5,000$ payments.

a$.$ How large must the deposit be$?$

b$.$ How much will be in the account immediately after you make the first withdrawal?

Stx years from today you need $$10,000.$ You plan to deposit $$1,500$ annually, with the first payment to be made a year from today, in an account that pays a $5\%$ efiective annual rate. Your last deposit, which will occur at the end of Year $6,$ will be for less than $$1,500$ if less is needed to reach $$10,000.$ How large will your last payment be$?$

Stmon recently received a credit card with an $18\%$ nominal interest rate. With the card, he purchased an Apple iPhone $11$ for $$700.$ The minimum payment on the card is $$20$ per month.

a$.$ If Simon makes the minimum monthly payment and makes no other charges, how many months will it bo bofore ho pays of the card?

b$.$ If Stmon makes monthly payments of $$70,$ how many months will it be before he pays ofiche debt?

c$.$ How much more in total payments will Simon make under the $920-$ a$-$month plan than under the $570-$a month plan? Make sure you use three decinal places for $N.$