$1.$ Five years ago, you bought a $$70,000$ house by putting $10\%$ down and financing the rest at a

rate of $8\mathrm{.}5\%$ for $30$ years. What is your monthly payment? How much interest did you pay on the

loan over the last year? Today you decide to refinance the house for $15$ years at a rate of $6\mathrm{.}25\%.$

The bank charges you transaction costs of $$1500$ which you include in the balance of the new

loan. What are your new monthly payments? $($Use excel for this question$)$

$2.$ A year ago an investor placed $$10,000$ in a savings account that was earning $5\%$ a year with

monthly compounding. After $3$ months the bank dropped the rate to $4\%$ a year and then three

months later dropped the rate to $3\%$ and finally after another $3$ months dropped the rate to its

current $2\%$ a year. How much money did the investor earn in interest over the last year?

$3.$ You decide you want to retire in $30$ years. You decide to invest $$5000$ at the end of each year

in a fund earning $8\%$ a year over the next $30$ years. How much money will you have at the end of

the $30$ years? Now assume each payment will be increased by $5\%$ a year, e$.$g$.$ the first payment

will actually be $$5250,$ the next payment $$5,512\mathrm{.}50,$ and so on$.$ How much money will you have

for retirement at the end of the $30$ years?

$4.$ You win the $$2$ million Georgia lottery. They promise you a payout of $$100,000$ a year for $20$

years. Knowing some finance you ask them for a lump sum payment today of $$1\mathrm{.}5$ million

instead of the $20$ yearly installments. You immediately take $$100,000$ out of the lump sum of

$$1\mathrm{.}5$ million and invest the rest for $19$ years at a rate of $5\%.$ If you withdraw $$100,000$ a year out

of this investment for the next $19$ years, how much will you have at the end of that period? Was

your idea a better way to take the payments? Explain your answer.

$5.$ A used car costs $$5000.$ The dealer says she can give it to you for no money down and $$150$ a

month for $60$ months. You have a credit card with a $$6000$ limit and an APR of $14\%.$ How do

you decide to finance the car? Explain your answer.

$6.$ A retiree is worried about the future purchasing power of her retirement money. She has

decided to buy a $30-$year growing annuity that starts with an initial payment of $$8,000$ a month

and increases at a rate of $0\mathrm{.}2\%$ a month. The appropriate discount rate is $10\%$ a year, how much

should she pay for it today? Given that amount, what was her required yearly return over the

previous $20$ years if she started with $$50,000(20$ years ago$)$ and contributed $$500$ a month to her

pension plan?

$7.$ You are offered an investment that gives you the following cash flow stream, $1000,2000,$

$3000,4000.$ They occur at the beginning of each year, starting now. if you could invest this

money at $12\%$ compounded monthly. What is the maximum you would pay for this investment.

$8.$ I plan to retire in $20$ years. I currently have $$150,000$ saved up$.$ I will invest $$1000$ at the

beginning of every month in the account. If I earn $10\%$ a year over the next ten years and then

$12\%$ a year over the remaining $10$ years, how much will I have for retirement? At retirement I

transfer all the money into assets that earn only $7\%$ a year. If I start withdrawing $$10,000$ at the

end of every month during retirement, how long before I run out of money? Explain your

answer.

$9.$ A recent college grad begins to invest $$200$ a month in a fund that earns $12\%$ a year with

monthly compounding. How much will she have after $35$ years? If she had started with the same

initial investment but increased the monthly amount by $0\mathrm{.}5\%$ each month, how long would it

take her to have the same future value? $(6$ points$)$

$10.$ Excel spreadsheet Question

Create a loan amortization chart on excel and answer the following question

A couple bought a $$100,000$ house six years ago using $10\%$ down and a $15$ year mortgage with

an annual interest rate of $7\mathrm{.}8\%.$ What are their monthly payments? What percentage of their total

payments over the last six years went to paying off the principal? Starting today the couple

decides to pay $$100$ extra on their monthly payment, how long will it take to pay off the house?