Final answer:
To determine the interest rate required for Calina to have $10000 after 10 years of semi-annual compounding, the interest rate is 4.93%.
Step-by-step explanation:
To determine the interest rate required for Calina to have $10000 after 10 years of semi-annual compounding, we can use the formula for compound interest:
Future Value = Principal * (1 + Interest Rate / Number of Compounding Periods)^(Number of Compounding Periods * Number of Years)
Let's plug in the given values:
Future Value = $10000, Principal = $6000, Number of Compounding Periods = 2 per year, Number of Years = 10
Rearranging the formula to solve for Interest Rate:
Interest Rate = ((Future Value / Principal)^(1 / (Number of Compounding Periods * Number of Years))) - 1
Substituting in the values:
Interest Rate = (($10000 / $6000)^(1 / (2 * 10))) - 1 = 0.0493 or 4.93%