Final answer:
To calculate the total present value of payments under the original contract, calculate the present value of each payment and sum them up. Do the same for the new payment structure. The difference in present values represents the change. Compare the total present values to evaluate the financial implications and benefits.
Step-by-step explanation:
To calculate the total present value of the payments Bob has to make to Jim under the original contract, we need to calculate the present value of each payment and then sum them up. The present value is calculated using the formula:
PV = FV / (1 + r)^n
where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods. For the first payment of $2946, which is due in 24 months, assuming an interest rate of 8%, the present value is calculated as:
PV = 2946 / (1 + 0.08)^24
Similarly, for the second payment of $3568, due in 39 months, the present value is:
PV = 3568 / (1 + 0.08)^39
To calculate the total present value of the payments Bob has to make under the new payment structure, we need to calculate the present value of the single payment of $1590 made today. Using the same formula as before, assuming an interest rate of 8%, the present value is:
PV = 1590 / (1 + 0.08)^0
The difference in present values between the original and new payment structures is the sum of the present values of the original payments minus the present value of the new payment. Finally, to evaluate the financial implications and benefits of the proposed change, we can compare the total present values and determine if it is more advantageous for Bob to make the new payment or stick with the original payment structure.