Final answer:
The present value of an annuity with hourly payments, given an annual interest rate, involves converting the annual rate to an hourly rate and using the present value of an annuity formula. However, the calculation can be approximated by summing the present values of each annual period using an adjusted version of the formula for discrete annual payments.
Step-by-step explanation:
To compute the present value of an annuity with hourly payments, we would normally use the present value of an annuity formula. However, because the payments are made hourly, we would first need to convert the annual interest rate to an hourly rate and then apply it to the formula. Since there are 8760 hours in a non-leap year, the hourly interest rate would be 1.6% divided by 8760. Nevertheless, the complexity of this calculation goes beyond typical high school mathematics, as standard financial formulas assume compounding on an annual, semi-annual, quarterly, or monthly basis, not hourly. Therefore, for simplicity, we can approximate this calculation by finding the present value for each annual period and then summing them.
Let's assume an annual interest rate of 1.6%. The formula for the present value of an annuity is:
PV = Pmt × ¶[1 - (1 + r)^{-n}]/r]
Where PV is the present value, Pmt is the payment per period, r is the interest rate per period, and n is the number of periods. For this problem, the payments (Pmt) add up to $0.59 × 8760 hours = $5168.40 per year. Assuming the 1.6% interest rate is compounded annually, the calculation must be adjusted accordingly:
First year's PV: $5168.40 / (1 + 0.016)^1
Second year's PV: $5168.40 / (1 + 0.016)^2
Then, we would sum these two present values to get the total present value of the annuity, rounding the final answer to the nearest dollar.