Question 423398: How do you solve for APR in this equation?
1.0593 = (1 + APR/3.3182)) ^3.3182
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! looks like you caught a tiger by the tail.
the easiest way to solve this is to let x = apr and let y = (1 + (x/3.3182))
your equation becomes:
1.0593 = y^3.3182
you can take the 3.3182 root of both sides of this equation to get:
1.0593^(1/3.3182) = y
use your calculator to get y = 1.017512898
your equation of 1.0593 = y^3.3182 is now equal to:
1.0593 = 1.017512898^(3.3182)
we original set y = 1 + x/3.3182
we know that y = 1.017512898
we can substitute for y to get:
1.017512898 = 1 + (x/3.3182)
subtract 1 from both sides of this equation to get:
.017512898 = x/3.3182
multiply both sides of this equation by 3.3182 to get:
x = .058111297 = apr
that should be your answer.
to confirm, plug that into your original equation to see if it is true.
your original equation is:
1.0593 = (1 + (APR/3.3182)) ^3.3182
replace apr with .058111297 to get:
1.0593 = (1 + (.058111297/3.3182)) ^(3.3182)
simplify to get:
1.0593 = 1.017512898^(3.3182)
simplify further to get:
1.0593 = 1.0593 confirming that the value of your apr that we calculated is good.
in your equation of:
1.0593 = y^3.3182
you could also have taken the log of both sides of the equation to get:
log(1.0593) = log(y^3.3182) which becomes:
log(1.0593) = 3.3182 * log(y)
divide both sides of the equation by 3.3182 to get:
log(1.0593) / 3.3182) = log(y)
simplify by taking the log of 1.0593 and dividing by 3.3182 to get:
log(y) = .007539923
take the anti-log of both sides of the equation to get:
y = 1.017512898
either way would have gotten you to y = 1.017512898
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