Answer:
let A = AAA bonds that yield 4%
let a = A bonds that yield 5%
let B = B bonds that yield 8%
A = 2B
A)
A + a + B = 28,000 (replace A with 2B)
0.04A + 0.05a + 0.08B = 1,460 (replace A with 2B)
2B + a + B = a + 3B = 28,000 ⇒ a = 28,000 - 3B
0.08B + 0.05a + 0.08B = 0.05a + 0.16B = 1,460 (replace a with 28,000 - 3B)
0.05(28,000 - 3B) + 0.16B = 1,400 - 0.15B + 0.16B =1,460
1,400 + 0.01B = 1,460
0.01B = 1,460 - 1,400 = 60
B = 60 / 0.01 = $6,000
A = $12,000
a = $28,000 - $6,000 - $12,000 = $10,000
AAA bonds = $12,000
A bonds = $10,000
B bonds = $6,000
B)
A + a + B = 38,000 (replace A with 2B)
0.04A + 0.05a + 0.08B = 1,990 (replace A with 2B)
2B + a + B = a + 3B = 38,000 ⇒ a = 38,000 - 3B
0.08B + 0.05a + 0.08B = 0.05a + 0.16B = 1,990 (replace a with 28,000 - 3B)
0.05(38,000 - 3B) + 0.16B = 1,900 - 0.15B + 0.16B =1,990
1,900 + 0.01B = 1,990
0.01B = 1,990 - 1,900 = 90
B = 90 / 0.01 = $9,000
A = $18,000
a = $38,000 - $9,000 - $18,000 = $11,000
AAA bonds = $18,000
A bonds = $11,000
B bonds = $9,000
