Multiple choice

A startup founder invests \$15,000 at an annual interest rate, compounded semiannually. The founder wants to earn at least \$3,150 in interest over one year. What is the least annual interest rate that would meet this goal?

  1. 20%

  2. 25%

  3. 27%

  4. 28%

  5. 32%
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A Correct answer
Explanation

Principal P = 15000, Interest I = 3150, Time t = 1 year, compounded semiannually (n=2). Formula: A = P(1 + r/2)^(2*1). 18150 = 15000(1 + r/2)^2. 1.21 = (1 + r/2)^2. 1.1 = 1 + r/2. r/2 = 0.1, so r = 0.2 or 20%.

AI explanation

Using the compound interest formula, the total amount must be at least $15,000 plus $3,150, which equals $18,150. Because the interest is compounded semiannually, this gives the equation 18150 = 15000 multiplied by (1 plus R/2) squared. Solving for the semiannual rate yields a factor of 1.1, meaning the semiannual rate is 10%; multiplying this by 2 gives the least annual interest rate of 20%.

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