Make sure you show the inputs you use for each problem. If you don$$t use a financial calculator, show the formulas that you used. Don$$t just give the final answer. Correct answers without showing the work receive only a portion of the full credit

For example: if the question asks you what is the present value of $$200$ that you will receive $5$ years later with an annual interest rate of $10\%?$ You can draw a time line like this:

$0$ i$=10\%$ N$=5$

$|--------------|$

$?200$

And your inputs will be

N $=5$; I$/$YR $=10$; PMT $=0$; FV $=200$; Solve for PV $=124\mathrm{.}1843$

$1.$ Douglas needs to borrow $$15,600$ today for his tuition bill. He agrees to pay back the loan in a lump$-$sum payment five years from now, after he is out of college. He bank states that the payment will need to be $$19,683.$ If Douglas borrows the $$15,600$ from the bank, what interest rate is he paying on his loan?

$2.$ Sarah$$s retirement goal is $$2,000,000.$ The bank is offering you a certificate of deposit that is good for forty years at $4\mathrm{.}7\%.$ What initial deposit does Sarah to make today to reach her $$2,000,000$ goal at the end of forty years?

$3.$ Steve wants to buy a saving bond for her newborn niece. The face value of the saving bond is $$1,000,$ the amount the niece would receive twenty years later. The government is currently paying $3\mathrm{.}5\%$ per year on savings bonds. How much is this saving bond cost today?

$4.$ Paul and Mary are looking for a vacation place. They find a small but pleasant condo in Malibu listed at $$534,000.$ They decide that now is not the right time to buy and that they will wait six years. The condos in Malibu appreciated each year at $3\%.$ What will, a similar condo sell for in six years?

$5.$ You are the planning commissioner for Springfield, a growing city in the Southwest. The city council has estimated that the city$$s population will increase very rapidly over the next twenty years, reaching an estimated $235,000.$ Today, the population is $105,680.$ What is the projected growth rate of this city?

$6.$ Lowe$$s has quoted a price of $$23,150$ to replace all the windows in Alex$$s home.. Five years ago, Alex put $$15,000$ into a home improvement account that has earned an average of $5\mathrm{.}5\%$ per year. Does Alex have enough money in his account to pay for the backyard fix$-$up$?$