Jerry is considering buying today a new bond which makes infinite annual payments. In particular the bond pays its holder 557.3 dollars one year from the day of purchase and the annual payment increases by 129.32 dollars each year thereafter. What is the maximum amount that Jerry should be willing to pay for this bond today given an annual interest rate of 6.91% ? (Accuracy is set at the second decimal.)

To calculate the maximum amount that Jerry should be willing to pay for the bond, we need to determine the present value of the infinite cash flow of annual payments.

The present value of cash flows can be calculated using the formula:

PV = C / (r - g),

where PV is the present value, C is the annual cash flow, r is the discount rate, and g is the growth rate of cash flows.

In this case, we have:
C = $557.3 (the first annual payment)
r = 6.91% (the annual interest rate)
g = 6.91% (the annual growth rate, which equals the interest rate)

Let's calculate the present value:

PV = $557.3 / (0.0691 - 0.0691) = $557.3 / 0 = undefined

Since the growth rate and the discount rate are equal, the present value calculation yields undefined. This means that the present value of an infinite cash flow cannot be determined using this formula.

In finance, there is a concept called perpetuity, which assumes that cash flows are received forever. However, the present value of a perpetuity can only be calculated if the cash flows are constant. In this case, since the cash flows are increasing every year, the present value cannot be calculated precisely.

Therefore, it is not possible to determine the maximum amount that Jerry should be willing to pay for the bond with the given information and approach.