if joe borrowed 931.00 dollars at a finance rate of 400% for 12 months what will be the finance charge for 1 month be?
want to know the finance charge for 1 month
since 400% is for the whole year, we divided the annual rate by 12 to get monthly finance rate:
400% / 12 ≈ 33.33% or .3333
.3333 * $931 = $310.33
I'm not sure what a finance rate is, but if it's anything like an interest rate, then read on.
This depends on how often we're compounding the interest. I'm assuming this is supposed to be compounded monthly.
Essientially you have some monthly interest rate, we'll call it x.
So, at the end of the first month, you owe $931(1+x).
Then at the end of the second month you're starting at 931(x+1), so after you apply the next month's interest, you now owe (931(x+1))(x+1)) = 931(x+1)^2.
Following the pattern, you end up with the equation 931(x+1)^12.
Since we know that we're paying 400% for the whole year we can say that 931(x+1)^12 = (1+4)*931 = 5*931, because 400% = 4, and we have to add the principle (100%) plus the interest (400%) for the year.
Next, take the 12th root of both sides, you get (931(x+1)^12)^(1/12) = (5*931)^(1/12).
The 12th power and 12th root cancel on the (x+1) term, leaving (x+1)(931^(1/12)) = (5*931)^(1/12).
Then if you divide both sides by (931^(1/12)), you get (x+1)(931^(1/12))/(931^(1/12)) = (5*931)^(1/12)/(931^(1/12)).
Notice that the terms on both the left hand side and the right hand side cancel, leaving x+1 = 5^(1/12). Subtract 1 and you get x = 5^(1/12) - 1.
But we're not done yet...
Remember that x was the interest rate for one month. And the the finance charge for the first month is going to be your principle times your rate.
So, we get a total interest for the first month of (931)*(5^(1/12) - 1). And if you can solve that in your head, I'll buy you a cookie. I would bust out the calculator here. And you should get $133.63, try it!
Notice that this is the the amount of interest accrued after one month, not the total bill. The total bill would be 931+133.63 = 1064.63. But the question was the finance charge for 1 month, and that should be $133.63.