SOLUTION: Angela currently has an account balance of $4,298.55. She opened the account 15 years ago with a deposit of $1,987.22. If the interest compounds monthly, what is the interest rate

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Angela currently has an account balance of $4,298.55. She opened the account 15 years ago with a deposit of $1,987.22. If the interest compounds monthly, what is the interest rate       Log On


   

Question 549804: Angela currently has an account balance of $4,298.55. She opened the account 15 years ago with a deposit of $1,987.22. If the interest compounds monthly, what is the interest rate on the account?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

A=P%281%2Br%2Fn%29%5E%28n%2At%29 Start with the compound interest formula


4298.55=1987.22%281%2Br%2F12%29%5E%2812%2A15%29 Plug in A=4298.55, P=1987.22, n=12 and t=15.


4298.55=1987.22%281%2Br%2F12%29%5E%28180%29 Multiply 12 and 15 to get 180.


4298.55%2F1987.22=%281%2Br%2F12%29%5E%28180%29 Divide both sides by 1987.22.


2.16309719105081=%281%2Br%2F12%29%5E%28180%29 Evaluate 4298.55%2F1987.22 to get 2.16309719105081.


root%28180%2C2.16309719105081%29=1%2Br%2F12 Take the 180th root of both sides.


1.00429553882184=1%2Br%2F12 Take the 180th root of 2.16309719105081 to get 1.00429553882184.


1.00429553882184-1=r%2F12 Subtract 1 from both sides.


0.00429553882183731=r%2F12 Combine like terms.


12%2A0.00429553882183731=r Multiply boths sides by 12 to isolate "r".


0.0515464658620477=r Multiply 12 and 0.00429553882183731 to get 0.0515464658620477.


r=0.0515464658620477 Rearrange the equation.


r=0.0515 Round to the nearest ten-thousandth.


So the interest rate is 5.15% (multiply by 100 to convert to a percentage)