Question 1040421: For a car loan using simple interest at a given rate, the amount of interest charged varies jointly with the loan amount (also known as the principal) and the time of the loan (in years). If a $10,000 car loan earns $1680 in simple interest over 6 years, how much interest will a $24,000 car loan earn over 7 years?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! simple interest formula is i = p * r * n
i is the interest
p is the principal
r is the interest rate per time period
n is the number of time periods.
in your problem:
p = 10,000
n = 6 years
i = 1680
the formula becomes 1680 = 10,000 * r * 6
solve for r to get r = 1680 / 10,000 / 6 = .028 per year.
if you loan 24,000 for 7 years, the formula of i = p * r * n becomes i = 24000 * .28 * 7 = 4704.
you were more then likely looking to use the joint variation formula of z = kxy.
in this formula, you would have needed to replace z with the interest of 1680 and x with the principal of 10,000 and y with the number of years of 6.
the formula would have become 1680 = k*10,000*6
you would have then solved for k to get k = 1680/(10,000*6) = .028
that would have been your constant of variation.
you would then have used the same formula of z = kxy, except you would have replaced k with .028 and x with 24,000 and y with 7 to get z = .028 * 24,000 * 7 which would have yielded z = 4704.
this is simply (or not so simply if you don't see it), the use of the joint variation formula to solve a simple interest formula.
the simple interest formula is, in effect, a joint variation formula with different names for each of the components.
joint variation formula is z = kxy.
simple interest formula is i = prn.
z=i
k=p
x=r
y=n
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