Multiple choice

Jessica made a deposit of \$7,500 at a 5% simple annual rate of interest. She also deposited another \$12,800 at a 4% annual rate of interest that was compounded quarterly. What was the approximate total amount of interest rounded to the nearest hundred that Jessica earned from these two deposits after 1 year?

  1. $900
  2. $1,000
  3. $1,200
  4. $1,400
  5. $1,700
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A Correct answer
Explanation

Interest 1: 7500 * 0.05 * 1 = 375. Interest 2: 12800 * (1 + 0.04/4)^4 - 12800 = 12800 * (1.01)^4 - 12800 = 12800 * 1.040604 - 12800 = 519.73. Total interest = 375 + 519.73 = 894.73. Rounded to the nearest hundred, this is 900.

AI explanation

Using the simple interest formula for the first deposit, the interest is (7500 * 5 * 1) / 100 which equals 375. Using the compound interest formula A = P(1 + R/400)^4 for the second deposit, the amount is 12800(1.01)^4 which equals approximately 13318.55, generating about 518.55 in interest. The total interest is 375 + 518.55 which equals 893.55. Rounding 893.55 to the nearest hundred gives 900.

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