Carlos bought a $235 water heater with his credit card. he used the water heater for five years before replacing it. he paid off the water heater after two years, making monthly payments. the water heater cost him an average of $1.56 per week in electricity, and $0.78 per week in water. if carlos’s credit card has an apr of 14.15%, compounded monthly, and he made no other purchases with it, what percentage of the lifetime cost of the water heater was interest? (round all dollar values to the nearest cent.)

First we will find the interest on:

P = $235 principal

t = 2 years

r = 0.1415 annual rate

A = future value 

I = A - P the interest

A = P(1 + r)^t

A = 235(1 + 0.1415)^2

A = $306.21

I = A - P

I = $306.21 - $235

I = $71.21

the interest was $71.21.

Next lets find the lifetime cost value:

Lifetime cost value = 306.21 + 5*1.56*52 + 5*0.78*52 = $914.61 (considering that 1 year = 52 weeks)

Now lets find the percentage what percentage the interest is of the lifetime cost:

(71.21/914.61)*100 = 7.79%

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.