Final answer:
When comparing the two investment options, 11.93% interest compounded continuously yields a slightly larger amount ($16,900.50) than the 12% interest compounded quarterly ($16,882.50) after one year.
Step-by-step explanation:
To determine which of the two investment options yields a larger amount after one year, we must calculate the future value for each scenario using the formulas for compound interest.
For the 12% interest compounded quarterly, the formula is Future Value = Principal * (1 + (rate / n))^(n*t), where 'Principal' is the initial amount, 'rate' is the annual interest rate, 'n' is the number of times interest is compounded per year, and 't' is the time in years. Plugging in our values:
Future Value = $15,000 * (1 + (0.12 / 4))^(4 * 1)
Future Value = $15,000 * (1 + 0.03)^(4)
Future Value = $15,000 * (1.03)^4
Future Value = $15,000 * 1.1255
Future Value = $16,882.50
For the 11.93% interest compounded continuously, the formula is Future Value = Principal * e^(rate*t), where 'e' is Euler's number (approximately 2.71828). So:
Future Value = $15,000 * e^(0.1193*1)
Future Value = $15,000 * 2.71828^(0.1193)
Future Value = $15,000 * 1.1267
Future Value = $16,900.50
Comparing the two future values, the option with 11.93% interest compounded continuously yields a slightly larger amount after one year than the option with 12% interest compounded quarterly.