Final answer:
To calculate the present value of an annuity with a variable interest rate, such as in the given scenario, one would perform separate present value calculations for each interest-rate period and add them together.
Step-by-step explanation:
The question given requires us to calculate the present value of an annuity. An annuity is a series of equal payments made at regular intervals, in this case, $2,600 monthly for 13 years. The interest rate is not constant; it changes from 10 percent compounded monthly for the first five years to 8 percent compounded monthly for the remaining term. To determine the present value of the annuity, we would use the present value formula for each segment of the annuity (first five years and the subsequent years) and then sum them up to get the total present value.
First, we would calculate the present value of the payments made in the first five years (60 monthly payments) using the 10 percent interest rate. Next, the present value of the remaining eight years (96 monthly payments) of payments is calculated using the 8 percent interest rate. Each of these calculations utilizes the present value of an ordinary annuity formula, which is PV = Pmt * [(1 - (1 + r)^(-n)) / r], where PV is the present value, Pmt is the payment amount per period, r is the interest rate per period, and n is the total number of payments.
To give an example similar to the bond scenario provided, if we had a simple two-year bond issuing a fixed payment at the end of each year with a given interest rate, we'd analyze the interest earned each year and apply the present value discount to calculate the bond's worth at the present rate. If the interest rates change, we do this calculation again with the new discount rate. This exercise is beneficial in understanding the calculation of present value with changing interest rates as it relates to the annuity question.