Question concerning interest?

Question

A city 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 7% 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 $34 million.

Answer 1

The amount required for  construction of  sports arena is $800 million

Let the amount from selling bonds is x at interest rate  7% 

Amount from insurance company is y  at interest rate 2%

x+y = 800

y = 800 - x   ------(1)

The annual interest for both bonds and insurance company is $34

0.07×x+0.02×y = 34  --------(2)

Put equation (1) in equation (2)

0.07x + 0.02(800 - x) = 34

0.07x +16 -0.02x = 34

0.05x = 18

x = 360

Put X value in equation (1)

y = 800 - 360

y = 440

The given limit for selling bonds is  x ≤ $480 million , but we take only $360 million

The given limit for  borrowing money from an insurance company is y ≤ $640 million ,but we take only $440 million

Hence the arena can be financed so that the annual interest is $34 million .