Chris has three options for settling an insurance claim. Option A will provide $1,500 a month for 6 years. Option B will pay $1,025 a month for 10 years. Option C offers $85,000 as a lump sum payment today. The applicable discount rate is 6.8 percent, compounded monthly. Which option should Chris select, and why, if he is only concerned with the financial aspects of the offers?

Question

Quizplus · Accepted Answer

To determine the best financial option, we calculate the present value (PV) of each option using the formula for the present value of an annuity: $ PV = P \times \left[ \frac{1 - (1 + r)^{-n}}{r} \right] $, where $P$ is the payment per period, $r$ is the monthly interest rate, and $n$ is the total number of payments. The discount rate is 6.8% annually, so the monthly rate is $ \frac{6.8\%}{12} = 0.5667\% $ or 0.005667.- For Option A: $ P = \$1,500 $, $ r = 0.005667 $, $ n = 6 \times 12 = 72 $  $ PV_A = \$1,500 \times \left[ \frac{1 - (1 + 0.005667)^{-72}}{0.005667} \right] \approx \$93,170.57 $- For Option B: $ P = \$1,025 $, $ r = 0.005667 $, $ n = 10 \times 12 = 120 $  $ PV_B = \$1,025 \times \left[ \frac{1 - (1 + 0.005667)^{-120}}{0.005667} \right] \approx \$87,665.93 $- Option C is already given as a lump sum of \$85,000 today, so its present value is \$85,000.Comparing the present values, Option A is approximately \$93,170.57, Option B is approximately \$87,665.93, and Option C is \$85,000. Therefore, Option A has the highest present value, but the correct choice is based on the largest value today, which is mistakenly identified in the choices provided. The explanation indicates Option A should be the correct financial choice based on the calculations, but the choice text mistakenly points to Option B for having the largest value today. Given the context of the explanation, the correct financial decision based on the present value calculations would favor Option A, but the provided choices and the question's framing suggest Option E (Option B: It has the largest value today) is the intended correct answer, which is a mistake in the context of the explanation provided.

Chris Has Three Options for Settling an Insurance Claim