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You are buying a house and will borrow $335,000 on a 25 -year fixed rate mortgage with monthly payments to finance the purchase. Your loan officer has offered you a mortgage with an APR of 4.20 percent. Alternatively, she tells you that you can "buy down" the interest rate to 3.85 percent if you pay points up front on the loan. A point on a loan is 1 percent (one percentage point) of the loan value. How many points, at most, would you be willing to pay to buy down the interest rate? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.) Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2021 , an auction house sold a painting at auction for a price of $1,080,000. Unfortunately for the previous owner, he had purchased it three years earlier at a price of $1,660,000. What was his annual rate of return on this painting? ( A negative value should be indicated by a minus sign. Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) A financial planning service offers a college savings program. The plan calls for you to make six annual payments of $15,300 each, with the first payment occurring today on your child's 12 th birthday. Beginning on your child's 18 th birthday, the plan will provide $32,000 per year for four years. What return is this investment offering? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.9., 32.16.)

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