Final answer:
To find the future value of Moira's $15,000 investment at a 7.5% semi-annual compound interest rate over 20 years use the future value formula with the adjusted semi-annual rate (3.75%) and 40 compounding periods.
Step-by-step explanation:
The student is asking how to calculate the future value of an investment made 20 years ago. Moira invested $15,000 at a semi-annual compound interest rate of 7.5%. To calculate the value of Moira’s investment today, we use the future value formula: Future value = Present value × (1 + Interest rate)number of compounding periods.
To apply this formula, first we need to adjust the annual interest rate to the semi-annual rate, which is half of 7.5%, so 3.75%. Next, because the interest is compounded semi-annually, there would be 2 compounding periods per year over 20 years, resulting in a total of 40 compounding periods.
Substituting the values into the formula gives us:
Future value = $15,000 × (1 + 0.0375)40
Calculating this gives us the future value of Moira’s investment today.