SOLUTION: 2. A business invests $8,000 in a savings account for two years. At the beginning of the second year, an additional $2,500 is invested. At the end of the second year, the account

Question 199561: 2. A business invests $8,000 in a savings account for two years. At the beginning of the second year, an additional $2,500 is invested. At the end of the second year, the account balance is $11,445. What was the annual interest rate?
Im not good at interest

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the interest formula. Note: since we're only concerned with year intervals, this means that (so we don't have to worry about exponents)

Plug in (since $8,000 is the original amount in the account)

Distribute

So after one full year, you now have dollars in the account.

Now because "an additional $2,500 is invested", this pushes up the amount to (just add 2500 to the last expression). Combine like terms to get

So the new principal is

Since after two years you have $11,445, this means that

Go back to the original formula

Plug in , and

FOIL

Subtract 11445 from both sides.

Combine like terms.

Notice we have a quadratic 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 Divide

So the possible answers are or

However, since you CANNOT have a negative interest rate, this means that the only possible answer is

Now multiply by 100 to get .

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Answer:

So the annual interest rate is 5%
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