Question

Assume that Austin Water purchases surface water from the Lower Colorado River Authority at a cost of $120,000 per month in the months of February through September. Instead of paying monthly, the utility makes a single payment of $880,000 at the end of the year (i.e., end of December) for the water it used. The delayed payment essentially represents a subsidy by the Authority to the water utility. At an interest rate of 3% per year compounded monthly, what is the amount of the subsidy?

Answer 1

At an interest rate of 3% per year compounded monthly, using the annuity formula the amount of the subsidy is:

$S = P * ((1 + i)^n – 1)/i - 880,000 = 120,000×((1 + 0.03/12)^8 - 1)/(0.03/12) - 880,000 = 88,442.13.$