Final answer:
To calculate the future value of an investment compounded monthly, the formula A = P(1 + r/n)^(nt) should be used. Ted's investment requires the use of the compound interest formula with monthly compounding, which is not among the provided choices, making 'None of the above' the correct answer.
Step-by-step explanation:
The question involves determining the future value of an investment using compound interest, where interest is earned on both the initial principal and the accumulated interest from previous periods. For Ted's investment of $1500 with a monthly compounding interest at a rate of 4.5% over 12 years, the correct formula to use is:
A = P(1 + r/n)nt
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount ($1500 in this case).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for in years.
In this case, A is the total amount after 12 years, P is $1500, r is 0.045 (4.5% expressed as a decimal), n is 12 (since interest is compounded monthly), and t is 12 years. Thus, the correct choice for Ted's situation is:
None of the above, because none of the offered formulas correctly represent the compound interest formula for monthly compounding. The closest correct formula would be:
A = 1500(1 + 0.045/12)12*12
This accounts for the monthly compounding by dividing the annual rate by 12 and then raising it to the power of the total number of compounding periods (12 months per year for 12 years).