A sum of $\$ 6,700$ is due for payment 2 years from now. If money is worth $5.8 \%$ compounded monthly, determine the equivalent value 8 years from now. a) $\$ 9,862.31$ b) $\$ 12,556.66$ c) $\$ 14,243.69$ d) $\$ 9,480.80$ e) $\$ 12,172.38$

Step 1 ：The problem is asking for the future value of a present sum of money, given a certain interest rate and time period. The formula for future value (FV) is: \(FV = PV * (1 + r/n)^{nt}\) where: PV is the present value (the initial amount of money), r is the annual interest rate (in decimal form), n is the number of times that interest is compounded per year, and t is the time the money is invested for, in years.

Step 2 ：In this case, PV = $6,700, r = 5.8% = 0.058, n = 12 (since interest is compounded monthly), and t = 8 years. We can plug these values into the formula to find the future value.

Step 3 ：The future value calculated is approximately $10,643.93. However, this value does not match any of the options provided in the question. The mistake is in the time period. The question asks for the equivalent value 8 years from now, but the sum is due for payment 2 years from now. So, the time period for which the money is invested should be 8 - 2 = 6 years, not 8 years. We need to correct this and calculate the future value again.

Step 4 ：With the corrected time period of 6 years, the future value calculated is approximately $9,480.80.

Step 5 ：Final Answer: The equivalent value 8 years from now is approximately \(\boxed{\$ 9,480.80}\). So, the correct option is (d) \(\boxed{\$ 9,480.80}\).