10.2 Personal Loans and Simple Interest 603 29. Pawning a Saxophone Elisa needs money to repair her home air conditioner, so she pawns her saxophone. The pawnbroker loans Elisa $270. Seven days later, Elisa gets her saxophone back by paying the pawnbroker $280.50. What annual simple interest rate did the pawnbroker charge Elisa? 200% 30. A Pawn Loan Jeffrey wants to take his mother out for dinner on her birthday, so he pawns his watch. The pawnbroker loans Jeffrey $75. Fourteen days later, Jeffrey gets his watch back by paying the pawnbroker $80.25. What annual simple interest rate did the pawnbroker charge Jeffrey? 180% 31. Purchase Option Comparison Sybil is buying a new chaise lounge that sells for $316 at two different stores. At Patios and More she has the option of paying $100 as a down payment and then paying $250 in 6 months. At Casual Outdoor Furniture she has the option of paying $150 as a down payment and then paying $200 in 9 months. a) Determine the annual simple interest rate charged by Patios and More. 31.48% b) Determine the annual simple interest rate charged by Casual Outdoor Furniture. 27.31% c) Which store charges the higher rate of simple interest? Patios and More 32. Loan Choices Thompson is considering adding a banquet room to his restaurant. The construction cost of the banquet room would be $30,000. DCR Construction offers Thompson the following terms: $10,000 as a down payment and $25,000 due in 24 months. MJV Construction offers Thompson the following terms: $12,000 as a down payment and $23,000 due in 30 months. a) Determine the annual simple interest rate charged by DCR Construction. 12.5% b) Determine the annual simple interest rate charged by MJV Construction. 11.1% c) Which company charges the higher rate of simple interest? DCR Construction 33. Bank Discount Note Julie borrowed $3650 from her bank for 18 months using a 7.6% discount note. a) How much interest did Julie pay the bank for the use of its money? $416.10 b) How much did she receive from the bank? $3233.90 c) What was the actual rate of interest she paid? 8.58% 34. Bank Discount Note Kwame borrowed $2500 for 5 months from a bank using a 2% discount note. a) How much interest did Kwame pay the bank for the use of its money? $20.83 b) How much did he receive from the bank? $2479.17 c) What was the actual rate of interest he paid? 2.02% In Exercises 35–38, determine the due date of the loan, using the exact time, if the loan is made on the given date for the given number of days. 35. May 31 for 150 days October 28 36. March 13 for 120 days July 11 37. November 25 for 120 days (the loan is due in a leap year) March 24 38. July 5 for 210 days January 31 In Exercises 39– 44, determine the exact time from the first date to the second date. Use Table 10.1. Assume the year is not a leap year unless otherwise indicated. 39. February 25 to May 5 69 days 40. July 5 to November 18 136 days 41. February 2 to October 31 (the loan is due in a leap year) 272 days 42. June 14 to January 24 224 days 43. August 24 to May 15 264 days 44. December 21 to April 28 128 days In Exercises 45– 48, if necessary round all dollar figures to the nearest cent. 45. Seed Loan On March 1, Burnette borrowed $3500 at an annual simple interest rate of 4.5% to pay expenses to plant his corn crop. After the harvest, on November 15, he repaid the loan plus the interest. a) Determine the length of the loan in days. 259 days b) Determine the amount of simple interest charged. $113.31 c) Determine the amount needed, including principal and interest, to pay off the loan. $3613.31 46. Play Production Loan On May 21, to help pay for a play production, Preston borrowed $15,000 at an annual simple interest rate of 6.75%. After a successful series of performances, Preston repaid the loan plus the interest on September 28. a) Determine the length of the loan in days. 130 days b) Determine the amount of simple interest charged. $365.63 c) Determine the amount needed, including principal and interest, to pay off the loan. $15,365.63 LightField Studios/Shutterstock
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