604 CHAPTER 10 Consumer Mathematics 47. Business Startup Loan On August 15, Anastasia borrowed $30,000 at an annual simple interest rate of 3.25% to start an after-school tutoring center. On June 21 of the following year, Anastasia repaid the loan plus the interest. Assume neither date was in a leap year. a) Determine the length of the loan in days. 310 days b) Determine the amount of simple interest charged. $839.58 c) Determine the amount needed, including principal and interest, to pay off the loan. $30,839.58 48. Business Startup Loan On November 1, Senia borrowed $50,000 at an annual simple interest rate of 5.5% to start a holiday decorating business. On March 1 of the following year, which was a leap year, Senia repaid the loan plus the interest. a) Determine the length of the loan in days. 121 days b) Determine the amount of simple interest charged. $924.31 c) Determine the amount needed, including principal and interest, to pay off the loan. $50,924.31 United States Rule In Exercises 49–58, a partial payment is made on the date(s) indicated. Use the United States rule to determine the balance due on the maturity date. Assume the year is not a leap year. Where appropriate, round interest calculations to the nearest cent. Principal Rate Effective Date Partial Payment(s) Amount Date(s) Maturity Date 49. $3200 3% June 1 $1200 July 1 Sep. 29 50. $5400 4% Jan. 20 $2500 Apr. 15 May 31 51. $2400 5.5% Feb. 1 $1000 May 1 Aug. 31* 52. $8500 11.5% Sep. 1 $4250 Oct. 31 Dec. 31* 53. $9000 6% July 15 $4000 Dec. 27 Feb. 1* 54. $1000 12.5% Jan. 1 $300 Jan. 15 Feb. 15* 55. $1800 15% Aug. 1 $500 Sept. 1 Nov. 1* $500 Oct. 1 56. $5000 14% Oct. 15 $800 Nov. 15 Jan. 1* $800 Dec. 15 57. $11,600 6% Mar. 1 $2000 Aug. 1 Dec. 1* $4000 Nov. 15 58. $21,000 4 %3 8 July 12 $8000 Oct. 10 Jan. 30* $6000 Dec. 8 59. Company Loan On March 1, the Zwick Balloon Company signed a $6500 note with simple interest of 10 %1 2 for 180 days. The company made payments of $1750 on May 1 and $2350 on July 1. How much will the company owe on the maturity date? $2646.24 60. Flag Company Loan On April 3, the Mears Flag Company borrowed $15,000 to pay for start-up costs for its new showroom. The loan had a simple interest rate of 8.25% and was for 270 days. The company was able to make partial payments of $6000 on May 28 and $3500 on October 12. How much will the company owe on the maturity date of the loan? $6084.41 Challenge Problems/Group Activities 61. U.S. Treasury Bills On November 14, Kris purchased a 364-day, U.S. Treasury bill with a face value of $1000 at a 5.05% discount (see Example 5). On the maturity date, Kris will receive $1000. Assume neither date was in a leap year. a) What is the maturity date of the Treasury bill? November 13 b) How much interest did the U.S. government pay Kris on the maturity date? $51.06 c) How much did Kris pay for the Treasury bill? $948.94 d) What is the actual rate of interest of the Treasury bill? Round the answer to the nearest hundredths of a percent. 5.32% 62. U.S. Treasury Bills On October 31, Brian purchased a 180-day, U.S. Treasury bill with a face value of $10,000 at a 5.56% discount (see Example 5 and Exercise 61). On the maturity date, Brian will receive $10,000. The bill due date is in a leap year. a) What is the maturity date of the Treasury bill? April 28 b) How much interest did the U.S. government pay Brian on the maturity date? $278 c) How much did Brian pay for the Treasury bill? $9722 d) What is the actual rate of interest of the Treasury bill? Round the answer to the nearest hundredths of a percent. 5.72% 63. Tax Preparation Loan Many tax preparation organizations will prepay customers’ tax refunds if they pay a one-time *See Instructor Answer Appendix 49. $2023.06 50. $2966.08 Photo travel VlaD/ Shutterstock
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