Question

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.)
a.
14.15%
b.
13.35%
c.
4.12%
d.
30.83%

Answer 1

Compute operating costs: weekly cost = $1.56 + $0.78 = $2.34. Over 5 years (5·52 = 260 weeks) that's 260·$2.34 = $608.40.

Credit-card math: monthly rate = 0.1415/12 = 0.0117916667. Monthly payment to amortize $235 over 24 months:
payment = 235·[r / (1 − (1+r)^−24)] ≈ $11.30 (rounded to the nearest cent).
Total paid = $11.30·24 = $271.20 → interest paid = $271.20 − $235.00 = $36.20.

Lifetime cost = purchase + interest + operating = $235.00 + $36.20 + $608.40 = $879.60.
Percent of lifetime cost that was interest = $36.20 / $879.60 ≈ 0.0412 = 4.12%.

Answer: c. 4.12%