Multiple choice

Sarah invested $Y in a special savings account that paid simple interest. The amount grew to \$5,000 after 2 years. Sarah then waited for another 3 years and got a final amount of \$8,000. At what annual interest rate did Sarah invest $Y initially?

  1. 33.33%

  2. 23.30%

  3. 18.0%

  4. 16.0%

  5. 16.5%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Simple interest for 3 years (from 5000 to 8000) is 3000. Interest per year = 1000. Principal Y = 5000 - (2 * 1000) = 3000. Rate = (Interest / Principal) * 100 = (1000 / 3000) * 100 = 33.33%.

AI explanation

Using the simple interest formula I = PTR/100, the interest earned over the first 2 years is (2 * Y * R)/100, making the total amount Y + (2 * Y * R)/100 = 5000. For the total 5 years, the interest is (5 * Y * R)/100, making the final amount Y + (5 * Y * R)/100 = 8000. Subtracting the first equation from the second shows that the interest for 3 years is 3000, meaning the interest for 1 year is 1000 and the interest for 2 years is 2000; therefore, the initial principal Y is 5000 minus 2000 which equals 3000. The annual interest rate is (100 * 100) / 3000, resulting in 33.33%.

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