SOLUTION: a business invests $8,000 in a savings account for 2 years. at the beginning of teh second year, an additional $2500 is invested. At the end of the second year, the account balance

Question 187174: a business invests $8,000 in a savings account for 2 years. at the beginning of teh second year, an additional $2500 is invested. At the end of the second year, the account balance is $ 11445. What was the annual interest rate?
So far I used the compounding interest formula where I = P(1 + r)^t
for the 1 st year's interest = (8000 + 8000r)
and for the second year's interest was (1st year's interest + [(8000+2500) + (8000r)(1 + r)^1] = total income after two years of 11445.
to set up my quadratic equation I combined like terms
8000 + 8000r + [(10500 + 8000r)(1 + r)] = 11445
8000 + 8000r + [10500 + 8000r + 10500r + 8000r^2] = 11445
combining terms 18500 + 26500r + 8000r^2 = 11445
or 8000r^2 + 26500r = 11445 - 18500 or -7055
8000r^2 + 26500r + 7055 = 0
at this point I get stuck because the numbers are too high in order to effectively use the quadratic formula to solve for r
I believe the answer is .05 or 5% annual interest rate..can you show me how you worked through the quadratic formula...
Thank you very much!
Kerry
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 looking at intervals of a year, this means that the value of "t" is 1 and simplifies to or

Plug in (the initial investment) and (since we want to find the amount at the end of the first year)

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 (this principal will be invested in the account for year #2)

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.

Rearrange the equation.

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 Divide

So the possible answers are or

However, since you CANNOT have a negative interest rate, this means that we can ignore .

So this means that the only answer is

Now multiply by 100 (to convert to a percentage) to get .

=============================================

Answer:

So the annual interest rate is 5%

That's quite a guess :)
RELATED QUESTIONS
I need help putting this word problem into equation form, can someone help me? A... (answered by ankor@dixie-net.com)

2. A business invests $8,000 in a savings account for two years. At the beginning of the (answered by jim_thompson5910)

can someone please help me solve this problem? 2. A business invests $10,000 in a... (answered by scott8148)

2. A business invests $10,000 in a savings account for two years. At the beginning of... (answered by jim_thompson5910)

2. A business invests $10,000 in a savings account for two years. At the beginning of... (answered by josmiceli)

Please Help with this one I have been trying to figure this out for a while. A... (answered by scott8148)

Please help me solve this problem. A business invests $8,000 in a savings account... (answered by Theo)

Could anyone help me explain set-up of this equation: A business invests $10,000 in a... (answered by vleith)

A business invests $10,000 in a savings account for two years. At the beginning of the... (answered by checkley71)

A business invests $10,000 in a savings account for two years. At the beginning of the... (answered by stanbon)