### Finance Problems In Tutorial Library

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### TITLE: Finance Problems

#### CLASS / COURSE: Finance

QUESTION DESCRIPTION:

1.    (15 Points) You need \$3,000 to buy a new stereo for your car. If you have \$1,200 to invest at 6% compounded annually, how long will you have to wait to buy the stereo?

2.   (25 Points) Suppose you buy a new Toyota for \$25,000. You obtain a 4-year amortized loan with equal annual payment beginning one year from today (i.e. first payment made one year from today). The quoted interest rate for the loan is 10%, compounded annually

1. How much will your annual payments be?
2. Please complete the attached amortization schedule
 Year 1 Year 2 Year 3 Year 4 Beginning Balance \$25,000 Interest Paid Total Payment Principal Paid Ending Balance \$0

1. Assume your car will lose 30% of its market value the first year and further lose \$4,000 each year thereafter (i.e. by the end of the first year, your used car can will be sold for \$25,000 × (1-30%) = \$17,500 on the used car market; and will be sold for \$17,500-\$4,000=\$13,500 on the used car market by the end of year 2; and so on).  How much will your used car be worth by the end of year 3 and year 4? Please fill the used car value in the market value schedule.

 Year 1 Year 2 Year 3 Year 4 Ending Car Value \$17,500 \$13,500

1. With auto loans, it is common for buyers to trade in their cars after the outstanding principal on the car loan exceeds the re-sale value of the used car. After which loan payment will it be profitable for you to trade-in your car? Why?  (hint: the car should be sold if it can be sold for more than the balance owed to the dealer)

3.    (30 Points) Denzel wishes to save money to provide for his retirement. Beginning one month from now, he will begin depositing a fixed amount into a retirement savings account that will earn 10% compounded monthly. He will make 420 such deposits. Then, one year after making his final deposit, he will withdraw \$75,000 annually for 20 years. The fund will continue to earn 10% compounded monthly. How much should the monthly deposits be for his retirement plan?

Extra Credit (10 points): a brain-teaser question

Inside a dark room there were 5 hats, three blue and two red. Three people walked into the room, each grabbed a hat and placed it UNSEEN on his head.  All know there were three blue hats and two red hats in the dark room.

Once out of the room, NO ONE can see his own hat. The first man looked at the other two, thought for a while, and said “Gee, I don’t know the color of my hat”. The second man heard this. He looked at other people’s hats, paused for a moment, and said “me neither”. The third man is blind. He heard the first two men, and said immediately “I know the color of my hat”.

What is the color of the third man’s hat (2 points)? And how did he know? Please provide your reasoning (8 points).

SOLUTION DESCRIPTION: Completed Solution is attached. Click on Buy button and then download file to get full solution.

SUBJECTS / CATEGORIES:
1. Finance
2. Financial Management
3. Accounting
4. Corporate Finance