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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

Respuesta :

Edufirst

Answer:

  • Option B. $1,025 a month for 10 years.

Explanation:

Calculate the present value of each option:

     [tex]\text{Monthly rate: } 6.8\%/12 = 0.068/12 = 0.005\overline 6[/tex]

Formula:

        [tex]PV=C\times \bigg[\dfrac{1}{r}-\dfrac{1}{r(1+r)^t}\bigg][/tex]

Where:

  • PV is the present value of the constant monthly payments
  • r is the monthly rate
  • t is the number of moths

1. Option A will provide $1,500 a month for 6 years.

         [tex]PV=$\ 1,500\times \bigg[\dfrac{1}{(0.005\overline 6}-\dfrac{1}{0.005\overline 6(1+0.005\overline 6)^{(6\times12)}}\bigg][/tex]

         [tex]PV=\$ 88,479.23[/tex]

2. Option B will pay $1,025 a month for 10 years.

         [tex]PV=$\ 1,025\times \bigg[\dfrac{1}{(0.005\overline 6}-\dfrac{1}{0.005\overline 6(1+0.005\overline 6)^{(10\times12)}}\bigg][/tex]

         [tex]PV=\$ 89,068.22[/tex]

3. Option C offers $85,000 as a lump sum payment today.

  • PV = $85,000

Conclusion:

The present value of the option B, $1,025 a month for 10 years, has a the greatest present value, thus since he is only concerned with the financial aspects of the offier, this is the one he should select.