Jay invests \( \$ 10,000 \) at \( 3 \% \) simple interest for 19 years. Round your answers to the nearest cent. (a) How much interest is earned over the 19 year period? (b) How much is in the account at the end of the 19 year period?

To find the total interest earned on Jay's investment, we can use the formula for simple interest, which is: \[ \text{Interest} = P \times r \times t \] where: - \( P \) is the principal amount (\$10,000), - \( r \) is the rate of interest (3% or 0.03), and - \( t \) is the time in years (19 years). Plugging in the values: \[ \text{Interest} = 10,000 \times 0.03 \times 19 = 10,000 \times 0.57 = 5,700 \] So, the interest earned over the 19-year period is \( \boxed{5,700} \). Now, to find the total amount in the account at the end of the 19 years, we add the principal and the interest: \[ \text{Total Amount} = P + \text{Interest} = 10,000 + 5,700 = 15,700 \] Therefore, the amount in the account at the end of the 19-year period is \( \boxed{15,700} \).