SOLUTION: 2. A business invests $10,000 in a savings account for two years. At the beginning of the second year, an additional $3500 is invested. At the end of the second year, the account

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# 2

Start with the given formula


Plug in


Distribute


So at the end of the first year, he has dollars in the account


Since "At the beginning of the second year, an additional $3500 is invested", this means that we simply add 3,500 to the amount to get


So at the beginning of the second year, he invests dollars


So this time


Go back to the given formula


Plug in (this is the amount that is in the account after the second year) and


FOIL


Subtract 15,569.75 from both sides


Combine like terms


Multiply every term by the 100 to clear the decimals.


Notice we have a quadratic equation in the form of where , , and


Let's use the quadratic formula to solve for r


Start with the quadratic formula


Plug in , , and


Square to get .


Multiply to get


Rewrite as


Add to to get


Multiply and to get .


Take the square root of to get .


or Break up the expression.


or Combine like terms.


or Simplify.


So the possible answers are or

which approximate to or


However, since a negative interest rate doesn't make much sense, this means that the only solution is which is the percentage 8.5%


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Answer:
So the interest rate is 8.5%