Acity government has approved the construction of an $800 million sports arena. up to $480 million will be raised by selling bonds that pay simple interest at a rate of 4% annually. the remaining amount (up to $640 million) will be obtained by borrowing money from an insurance company at a simple interest rate of 2%. determine whether the arena can be financed so that the annual interest is $22 million. (if there is no solution, enter no solution.)

borrowing structure:

500 insruance at 2%

300 bonds at 4%

weighted average rate: 2.75%

Explanation:

we will calculate which rate generates an interes texpense of 22 million per year:

22,000,000 / 800,000,000 = 0,0025 = 2.75%

we need a weighted average rate for 2.75%

we construct an equation system:

insurnace company = 800 - bonds

we now solve for bond quantity:

B = 6/0.02  = 300

now we got bonds borring we calcualte for insurance borrowing:

800 - 300 = 500 million

we check:

300,000,000 x 0.04 = 12,000,000 interest

500,000,000 x 0.02 = 10,000,000 interest

                      total        22,000,000 interest

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