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

Question 155377: 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 balance is $15,569.75. What was the annual interest rate?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 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%

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