Question

jim wants to start investing in bonds. he checks with two brokers to ask them for suggestions of bonds to buy. broker j, who charges a commission of 3.6% of the market value of all bonds sold, recommends for jim to buy three par value $500 bonds from the city of danville, a par value $1,000 bond from raxin accounting, and two par value $1,000 bonds from united rotators. danville bonds are selling at 114.212, raxin accounting bonds are selling at 79.941, and united rotators bonds are selling at 102.844. broker k, who charges a fee of $28 for each bond sold, recommends that jim buy five par value $500 bonds from fort bend county, a par value $1,000 bond from the u.s. treasury, and two par value $500 bonds from iwad records. fort bend bonds are selling at 91.090, treasury bonds are selling at 101.163, and iwad records bonds are selling at 107.252. based on the current information, which brokers bond package will cost jim less money up front, and how much less will it cost him? a. broker js suggestion will cost jim $59.57 less than broker ks suggestion. b. broker js suggestion will cost jim $62.00 less than broker ks suggestion. c. broker ks suggestion will cost jim $148.57 less than broker js suggestion. d. broker ks suggestion will cost jim $208.07 less than broker js suggestion.

Explanation:

Step1: Calculate cost for Broker J

First, find the market value of each bond type. For Danville: 3 bonds, par $500, selling at 114.212. Market value per bond: $500 (114.212/100) = $571.06. Total for 3: 3*571.06 = $1713.18. Raxin: 1 bond, par $1000, selling at 79.941. Market value: $1000(79.941/100) = $799.41. United Rotators: 2 bonds, par $1000, selling at 102.844. Market value per bond: $1000*(102.844/100) = $1028.44. Total for 2: 21028.44 = $2056.88. Total market value: 1713.18 + 799.41 + 2056.88 = $4569.47. Commission: 3.6% of 4569.47 = 0.0364569.47 ≈ $164.50. Total cost for J: 4569.47 + 164.50 ≈ $4733.97.

Step2: Calculate cost for Broker K

Fort Bend: 5 bonds, par $500, selling at 91.090. Market value per bond: $500(91.090/100) = $455.45. Total for 5: 5*455.45 = $2277.25. Treasury: 1 bond, par $1000, selling at 101.163. Market value: $1000(101.163/100) = $1011.63. Iwad: 2 bonds, par $500, selling at 107.252. Market value per bond: $500*(107.252/100) = $536.26. Total for 2: 2*536.26 = $1072.52. Total market value: 2277.25 + 1011.63 + 1072.52 = $4361.40. Fee: $28 per bond, total bonds: 5+1+2=8. Fee total: 8*28 = $224. Total cost for K: 4361.40 + 224 = $4585.40.

Step3: Find difference

Subtract K's cost from J's: 4733.97 - 4585.40 ≈ $148.57. Wait, no—wait, K's cost is lower? Wait, 4585.40 vs 4733.97. So K is cheaper by 4733.97 - 4585.40 ≈ $148.57.

Answer:

c. Broker K’s suggestion will cost Jim $148.57 less than Broker J’s suggestion.