SAT Math Multiple Choice Question 462: Answer and Explanation

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Question: 462

12. When most people buy a house, they take out a mortgage to cover at least part of the cost of the home and then pay the loan back over time. The most common kind of mortgage is a 30-year loan. A couple buys a home and takes out a 30-year loan in the amount of $220,000 (called the principal). They decide they want to pay it off early to save money on interest. They set a goal of reducing the principal amount of the loan to $170,000 in four years. Suppose during the first two years of their four-year timeline, the couple pays down the loan by 10%. By what percent do they need to pay down the rest of the loan to reach their overall goal?

  • A. 10%
  • B. 14%
  • C. 18%
  • D. 20%

Correct Answer: B

Explanation:

B

Difficulty: Medium

Category: Problem Solving and Data Analysis / Rates, Ratios, Proportions, and Percentages

Strategic Advice: A question like this requires planning. Start by figuring out how much of the loan the couple has already paid down and how much they still have left to meet their goal.

Getting to the Answer: If they have reduced the principal amount by 10%, they have paid the loan down to 100 – 10 = 90% of its original value. Use the formula Percent × whole = part to get $220,000 × 0.9 = $198,000 remaining on the principal. So, after two years, the value of the loan is $198,000, which means the couple still have $198,000 – $170,000 = $28,000 of the principal loan amount left to pay off to reach their goal. Now, determine what percent of the remaining whole this constitutes using the same formula again. The percent is unknown this time, so call it p:

Therefore, the couple needs to pay down approximately 14% of the current principal amount to reach their goal.

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