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Mark has $100,000 to invest. His financial consultant advises him to diversify his investment in three types of bonds: short-term, intermediate-term, and long-term. The short-term bonds pay 4%, the intermediate-term bonds pay 6%, and the long-term bonds pay 7% simple interest per year. Mark wishes to realize a total annual income of 5.8%, with equal amounts invested in short- and intermediate-term bonds. How much should he invest in each type of bond?

Respuesta :

jepessoa

Answer:

Mark should invest:

  • $30,000 in short term bonds
  • $30,000 in intermediate term bonds
  • $40,000 in long term bonds

Explanation:

S = short term bonds

I = intermediate term bonds

L = long term bonds

S + I + L = 100,000

0.04S + 0.06I + 0.07L = 0.058 x 100,000 = 5,800

S = I

2S + L = 100,000

L = 100,000 - 2S (now we replace both I and L)

0.04S + 0.06s + 0.07(100,000 - 2S) = 5,800

0.1S + 7,000 - 0.14S = 5,800

7,000 - 5,800 = 0.14S - 0.1S

1,200 = 0.04S

S = 1,200 / 0.04 = 30,000

I = 30,000

L = 100,000 - 60,000 = 40,000

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