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InstructionMultiple Choice

Long Term Purchases

Question 1 • 26-27 Ignite Technical Math-Financial Math - MA2007

Olivia bought a $1,874 sprinkler system with her credit card. Her credit card has an APR of 10.31%, compounded monthly. She made no other purchases on the card until the sprinkler system was fully paid for, which took four years of identical monthly payments. Over the eight years that Olivia kept the sprinkler system, it used an average of $2.11 in water per week. After eight years, what percentage of the total lifetime cost of the system did the original price make up? (Round all dollar values to the nearest cent.)

Answer
A
81.66%
B
59.07%
C
38.25%
D
72.33%

Explanation

The monthly interest rate is 10.31% ÷ 12. Using the loan-payment formula for 48 monthly payments on $1,874 gives a payment of about $47.83, or about $2,295.84 total in payments. Water costs $2.11 × 52 × 8 = $877.76, so the total lifetime cost is $3,173.60. The original price’s share is $1,874 ÷ $3,173.60 × 100 ≈ 59.07%, which is choice B.

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