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

Algebra ->  Quadratic Equations and Parabolas -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
# 2

A=P%281%2Br%29 Start with the given formula


A=10000%281%2Br%29 Plug in P=10000


A=10000%2B10000r Distribute


So at the end of the first year, he has 10000%2B10000r 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 10000%2B10000r to get 10000%2B10000r%2B3500=13500%2B10000r


So at the beginning of the second year, he invests 13500%2B10000r dollars


So this time P=13500%2B10000r


A=P%281%2Br%29 Go back to the given formula


15569.75=%2813500%2B10000r%29%281%2Br%29 Plug in A=15569.75 (this is the amount that is in the account after the second year) and P=13500%2B10000r


15569.75=13500%2B13500r%2B10000r%2B10000r%5E2 FOIL


0=13500%2B13500r%2B10000r%2B10000r%5E2-15569.75 Subtract 15,569.75 from both sides


A=10000r%5E2%2B23500r-2069.75 Combine like terms


A=1000000r%5E2%2B2350000r-206975 Multiply every term by the 100 to clear the decimals.


Notice we have a quadratic equation in the form of ar%5E2%2Bbr%2Bc where a=1000000, b=2350000, and c=-206975


Let's use the quadratic formula to solve for r


r+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


Plug in a=1000000, b=2350000, and c=-206975


Square 2350000 to get 5522500000000.


r+=+%28-2350000+%2B-+sqrt%28+5522500000000--827900000000+%29%29%2F%282%281000000%29%29 Multiply 4%281000000%29%28-206975%29 to get -827900000000


r+=+%28-2350000+%2B-+sqrt%28+5522500000000%2B827900000000+%29%29%2F%282%281000000%29%29 Rewrite sqrt%285522500000000--827900000000%29 as sqrt%285522500000000%2B827900000000%29


r+=+%28-2350000+%2B-+sqrt%28+6350400000000+%29%29%2F%282%281000000%29%29 Add 5522500000000 to 827900000000 to get 6350400000000


r+=+%28-2350000+%2B-+sqrt%28+6350400000000+%29%29%2F%282000000%29 Multiply 2 and 1000000 to get 2000000.


r+=+%28-2350000+%2B-+2520000%29%2F%282000000%29 Take the square root of 6350400000000 to get 2520000.


r+=+%28-2350000+%2B+2520000%29%2F%282000000%29 or r+=+%28-2350000+-+2520000%29%2F%282000000%29 Break up the expression.


r+=+%28170000%29%2F%282000000%29 or r+=++%28-4870000%29%2F%282000000%29 Combine like terms.


r+=+17%2F200 or r+=+-487%2F200 Simplify.


So the possible answers are r+=+17%2F200 or r+=+-487%2F200

which approximate to r=0.085 or r=-2.435


However, since a negative interest rate doesn't make much sense, this means that the only solution is r=0.085 which is the percentage 8.5%


-----------------------------------------------------

Answer:
So the interest rate is 8.5%