How do you isolate a variable using the compound interest formula with no numbers? So for example how do i isolate P using this equation `A=P(1+i)^n?`
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Isolate a variable means to get it alone, or, in other words, solve for it. To achieve this, we can perform some operations on both sides of an equation, which lead to an equivalent equation. For example, we can add the same value to both sides, or multiply by the...


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Hello!

Isolate a variable means to get it alone, or, in other words, solve for it. To achieve this, we can perform some operations on both sides of an equation, which lead to an equivalent equation. For example, we can add the same value to both sides, or multiply by the same nonzero value.

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Solving this equation for `P` is simple, just divide both sides by `(1+i)^n:`

`A/(1+i)^n = P,` or `P=A(1+i)^(-n).`

 

Probably a more difficult task is to solve for `n.` For this, divide by `P:` `A/P=(1+i)^n.` Now we have to apply logarithm:

`ln(A/P)=ln((1+i)^n)=n ln(1+i).`

So `n=ln(A/P)/(ln(1+i)).`

Or, for `i,` `ln(1+i)=(ln(A/P))/n,` so `i=e^((ln(A/P))/n)-1.`

 

Which can be simplified to `i = (A/P)^(1/n) - 1`

 


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