Final answer:
To find the future value of quarterly $100 payments compounded at 7% quarterly for 10 years, use the future value of an annuity compound quarterly formula. The answer will represent the total value including interest on January 1, 2005.
Step-by-step explanation:
To find the value on January 1, 2005, of quarterly payments of $100 for 10 years at 7% compounded quarterly, we will use the formula for the future value of an annuity compound quarterly:
FV = P × {[(1 + r/n)^(nt) - 1] / (r/n)}
Where:
- FV is the future value of the annuity.
- P is the quarterly payment amount.
- r is the annual interest rate (in decimal form).
- n is the number of times the interest is compounded per year.
- t is the total number of years.
For this question, P = $100, r = 0.07, n = 4 (since the interest is compounded quarterly), and t = 10 years. Plugging these values into the formula gives us the future value which represents the total amount that will be in the account on January 1, 2005, including compounded interest.