Final answer:
The question pertains to finding the value of a future payment based on the principle of the time value of money, requiring the use of present value formulas. However, the interest rate is not provided, so a numerical answer cannot be calculated without it.
Step-by-step explanation:
The student's question is related to the concept of time value of money, which is a principle that money available now is worth more than the same amount in the future due to its potential earning capacity. This is a foundational concept in finance and is typically covered in high school and college math courses, specifically in financial math or algebra.
To solve the given problem, we need to find the present value of the single payment of $9463.53 and equate it to the sum of the present values of the two payments: one that has already been made a year ago ($3308.68) and another that is due in 9.8 years. This requires the use of the formula for calculating the present value of a lump sum given a specific interest rate, which is not provided in the question. If the question provided an interest rate, we would apply the present value formula:
PV = FV / (1 + i)^n
Where:
- PV is the present value
- FV is the future value, which is the amount of the payment
- i is the interest rate per period
- n is the number of periods
Without the interest rate, we cannot provide a numerical answer. However, once the rate is known, the student will be able to calculate the present value of each payment, set them equal to one another, and solve for the unknown future payment amount.