Problem Set 2
1a. In 1624, the Algonquin Indians sold the island of Manhattan to Peter Minuit for $24. Usually regarded as the great bargain of history, you might want to see how else this money could have earned dividends. Had the $24 been invested at 8 percent, compounded annually, what would it be worth today?
1b. What if that $24 had been invested, again at 8 percent, but compounded quarterly?
2. For your high school graduation present you receive a $10,000 US Savings Bond. You note that it matures in 15 years, and carries with it a 4.7 percent interest rate. You need some fast cash so that you can go off to the Jersey Shore and celebrate with some friends. What can you expect to get for your bond right now?
3 You take a partial ownership stake in a used book store which pays you 10 percent of all profits for the first five years. In those five years you receive profit sharing checks as follows: $4,720, $7,290, $12,400, $15,330, and $21,490. Using a competitive interest rate of 6 percent, what should you have paid, at maximum, for your 10 percent share?
4. You are thinking of buying a business with the expected following profits:
Year 1: $20,000
Year 2: $45,000
Year 3: $80,000
Year 4: $105,000
Year 5: $115,000
Year 6-10: $130,000
Using a competitive rate of interest of 7.5 percent, what is a reasonable price to pay for the business? (This one is a bit tricky)
5. At 25 you receive access to a trust fund set up by your grandfather, which will provide you with $30,000 per year for the rest of your life. Given a rate of 6 percent, what is the value of this package when you are born?
6. You are trying to get ahead of your daughter’s college tuition. You expect that when she starts college, in ten years, it will cost $22,000 per year. How much money do you need to bank today if you want to take care of that obligation? Use a competitive interest rate of 6.5 percent.
7. You win the PowerBall lottery which carries with it a $25 million dollar prize, payable in semi-annual payments over 20 years. If the state uses a current competitive interest of 6 percent, what is the value of a lump-sum payment?
a. If combined federal and state income taxes on the prize is 38 percent, what is the current lump sum payment?
b. If you take the lump sum payment (after taxes) and invest it aggressively at 9 percent (compounded annually), what will it be worth in 20 years?
8. It is Thanksgiving, and you are signing your kids up for summer camp for the following summer. The total comes to $5,000, due at the start of camp (July 1). The camp tells you that if you pay the total bill by January 1, they will discount it to $4,800. Current competitive rate of interest is 8 percent and your bank compounds monthly. Is this a good deal?
9. You finish graduate school at age 27, get a job, and start saving responsibly for retirement. You put away $5,000 each year. If you can earn 8.5 percent on your investment (compounded quarterly), how much will you have saved when you retire at age 65?
10. What is the correct price for a 20-year, 6.75%, $10,000 bond which pays quarterly interest, if the current competitive rate of interest on such bonds is 5.25%?
11. You buy a new Chevy Volt plug-in hybrid automobile, and finance it with a $25,000 car loan. The loan is to be paid off over 6 years and is offered at 4.25%. You will need to make 72 identical car payments. Without using a mortgage chart, can you figure out your monthly car payment?
