sierramay77
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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.)

Verified Answer :

azamunoz

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 + 51.5652 + 50.7852 = $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%

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The percentage of the lifetime cost of the water heater was \(7.78\%\) .

What is compound interest ?

Compound interest is the interest on principal which is charged on both the initial principal and the interest from previous periods.

\(Amount = P(1+\frac{R}{100} )^t\),

Here, \(P= Principal,\)

         \(R= Rate\)  and \(t=time\)

We have,

Cost of Water Heater \(=\$ 235\)

Water heater cost an average  in electricity  \(=\$1.56\) per week

Water heater cost an average  in water  \(=\$0.78\) per week

APR of credit card \(=14.15\%\) compounded monthly

Now,

Find Amount which was compounded,

\(Amount = P(1+\frac{R}{100} )^t\)

\(A=235(1+\frac{14.15}{100} )^2\)

\(A=306.20\)

Now,

So, Total Interest was charged ;

\(Interest=Amount - Principal\)

\(I = 306.20-235\)

\(I=71.2\),

To find the lifetime cost;

Heater was used for \(5\) years,

\(1\ Year =52\ weeks\)

So,

Cost of electricity \(= 5\ year * 52\ week\ *\ \$ 1.56=\$405.6\)

Cost of water  \(= 5\ year * 52\ week\ *\ \$ 0.78=\$202.8\)

So,

Total lifetime cost \(= 306.2+405.6+202.8=\$914.6\)

Now,

The percentage of lifetime cost as interest;

Percentage \(=\frac{Percentage}{Total\ cost} *\ 100\)

                   \(=\frac{71.2}{914.6} *100\)

Percentage  \(=7.78\%\)

Hence, we can say that the percentage of the lifetime cost of the water heater was \(7.78\%\) .

To know more about Compound interest click here

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