How Do You Algebraically Solve for n in Compound Interest Equations?

  • Thread starter e^(i Pi)+1=0
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In summary, the conversation discusses the equation 125,000 = 79,770.26(1 + 0.045/n)10n and finding a solution for n. It is mentioned that n = 12 is a solution for sufficiently large values of 12, but not an exact solution and that numerical techniques will need to be used. The conversation concludes with some humorous comments about the value of n.
  • #1
e^(i Pi)+1=0
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1

Homework Statement


125,000=79,770.26(1+[itex]\frac{.045}{n}[/itex])10n

Homework Equations


The Attempt at a Solution


I'm not sure how to use a logarithm with this, or if it's even possible. I know that n=12, I just don't know how to solve for it.
 
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  • #2
e^(i Pi)+1=0 said:
I know that n=12, I just don't know how to solve for it.
n = 12 is a solution for sufficiently large values of 12. n=12 (exactly) is not a solution. n≈12.06655246 is a solution.

You can't solve this analytically. You will need to resort to numerical techniques.
 
  • #3
Thanks, I wasn't sure if I was missing something. It's not exactly 12 here because the 79,770.26 is rounded.
 
  • #4
79,770.62 is closer, and 79,770.63 is closer still for n=12.
 
  • #5
D H said:
n = 12 is a solution for sufficiently large values of 12

:smile:
 
  • #6
D H said:
n = 12 is a solution for sufficiently large values of 12.

Nice! :biggrin:
 

FAQ: How Do You Algebraically Solve for n in Compound Interest Equations?

How do I solve for the unknown variable in an algebraic equation?

In order to solve for the unknown variable in an algebraic equation, you need to isolate the variable on one side of the equation by using inverse operations. This means using addition and subtraction to isolate the variable on one side, and multiplication and division to isolate it on the other side.

What are the steps to solve an algebraic equation?

The first step is to simplify the equation by combining like terms. Then, use inverse operations to isolate the variable. Next, solve for the variable by performing the necessary operations. Finally, check your answer by plugging it back into the original equation.

Can you solve an algebraic equation without using numbers?

Yes, you can solve an algebraic equation without using numbers by using variables to represent unknown quantities. This allows you to solve for an unknown value using symbols and equations.

How do I know if my solution to an algebraic equation is correct?

To check if your solution is correct, you can plug the value back into the original equation and see if both sides of the equation are equal. If they are, then your solution is correct.

What is the difference between solving an algebraic equation and simplifying an expression?

Solving an algebraic equation means finding the value of the unknown variable, while simplifying an expression means reducing an expression to its most basic form by combining like terms and performing operations. Solving an equation involves finding a specific value, while simplifying an expression does not necessarily yield a specific value.

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