[疑難] Quantitative Analysis

1.You just won the Florida lottery, which is currently at $45 million, by picking
the numbers 5, 13, 26, 28, 37, and 48. If you can earn an average yearly rate of
return equal to 6 percent, compound monthly, what would the lump-sum
payment have to equal for you to choose the lump-sum payment rather than a
30 annuity payments of $1.5 million each, with the first payment received
immediately?

2.Five years ago you purchased a house for $200,000. To buy the house, you
borrowed $180,000 at an average yearly rate of 7.2 percent. The mortgage has a
life of 15 years when you bought the house, and it required monthly payments.
Because you have been so successful in your career, you have decided that you
would like to pay off the mortgage. How much do you owe on the mortgage
today (five years after you bought the house)?

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