The Espedido family property taxes, amounting to $2,450, are due on July 1. If the taxes are instead paid 8 months in advance and the city can earn 6% interest per annum compounded monthly on surplus funds, what amount should the city accept now as an equivalent payment?

Introduction:
This problem involves finding the present value of a future payment when interest is compounded monthly. The property tax payment of $2,450 is due on July 1, but if it is paid 8 months earlier, we need to discount it using the monthly interest rate that the city can earn on surplus funds.

Given Data / Assumptions:

• Future payment (F) = $2,450 due at a future date.
• Time in advance = 8 months before the due date.
• Annual nominal interest rate R = 6% per annum.
• Compounding frequency = monthly (12 times per year).
• We want the equivalent present value (P) that will grow to $2,450 in 8 months at this interest rate.

Concept / Approach:
For compound interest with m compounding periods per year, the periodic rate i is:
i = R / (100 * m)The future amount F after n periods is:
F = P * (1 + i)^nWe know F and i and n, and need P, so we rearrange:
P = F / (1 + i)^nHere m = 12 and n = 8 months, so n = 8 periods.

Step-by-Step Solution:
Step 1: Compute the monthly rate: i = 6% / 12 = 0.5% per month = 0.005 in decimal form.Step 2: Identify the number of months until the due date: n = 8 months.Step 3: Use present value formula: P = F / (1 + i)^n.Step 4: Substitute values: P = 2,450 / (1.005)^8.Step 5: Calculate (1.005)^8 which is approximately 1.0407.Step 6: Divide: P ≈ 2,450 / 1.0407 ≈ 2,354.17.Therefore, the city should accept approximately $2,354.17 as an equivalent early payment.

Verification / Alternative check:
To verify, we can grow $2,354.17 forward for 8 months at 0.5% per month. Multiply by (1.005)^8 and we get back very close to $2,450, confirming that this is the correct discounted value.

Why Other Options Are Wrong:
Values like $2,376 and $2,389 are larger than the correct present value and would grow to more than $2,450, overcompensating the city. The figure $2,354 without cents is a rounded version that slightly underestimates the proper calculation. $2,300 is much too small and would not grow to the full tax amount. The only precisely correct option is $2,354.17.

Common Pitfalls:
One common mistake is to compute simple interest instead of compound interest, or to use the annual rate directly without dividing by 12 for monthly compounding. Another pitfall is treating 8 months as 8 years, which drastically distorts the result. Always convert the nominal annual rate to a periodic rate consistent with the time unit used in the number of periods.

Final Answer:
If the taxes are paid 8 months in advance, the city should accept approximately $2,354.17 as an equivalent payment at 6% per annum compounded monthly.