given a loan on $6000, interest is 2%, how much would have to be paid monthly in order to pay off the loan?i know the question is really simple, but which equation to impliment it completely...

The principal (P) is $6000 and the interest rate (r) is 0.02.

Now if the loan was for 1 month we would have

`L=P(1+r)` or `P=L/(1+r)`

If the loan was for 2 months we would have

`(1+r)((1+r)P-L)=L` or  `(1+r)^2P-(1+r)L=L` which gives `P=L/(1+r)+L/(1+r)^2`

So if the loan is n months we would have

`P = sum_(j=1)^n L/(1+r)^j=L sum_(j=1)^n 1/(1+r)^n`

We can solve this by noting that

`(1+r)P=L sum_(j=0)^(n-1) 1/(1+r)^n`

So

`(1+r)P - P = rP = L(1-1/(1+r)^n)`

So `L=(rP)/(1-1/(1+r)^n)`

Substituting P = $6000, r = 0.02 and n = 24

`L = (0.02(6000))/(1-1/(1-0.02)^24)`

Evaluating we get $317.23 per month.  Now this does seem high since 6000/24=250 but 2% per month is 48% for the entire loan, so this is actually a high interest rate made more attractive by stating it as a monthly interest rate.

So the final answer is $317.23 will pay off the loan in 24 months.