Question

You just received an insurance settlement offer related to an accident you had three years ago. The offer provides you with three choices: Option A: $1,500 a month for 6 years Option B: $1,025 a month for 10 years Option C: $85,000 as a lump sum payment today You can earn 7.5 percent on your investments and do not care if you personally receive the funds or if they are paid to your heirs should you die within the settlement period. Which option should you select and why is that option justified?

Answer 1

Answer:

It will be a better offer the option B because it yield a higher net present value at the given rate.

B 88,457

A 86,755

C 85,000

Explanation:

We are going to compare the present value of each annuity at the cost of capital rate 7.5%

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

option A

C= couta, monthly payment 1,500

rate= 0.075 is an annual rate we divide by 12 to get the monthly rate

time = 6 years = 6*12 = 72 months

$1,500 \times \frac{1-(1+0.075/12)^{-6*12} }{0.075/12} = PV$

option A PV = 86,754.78646

option B

C = 1,050

time = 10 years

same rate

$1,050 \times \frac{1-(1+0.075/12)^{-10*12} }{0.075/12} = PV$

option B PV =  88,456.97984

option C = 85,000

It will be a better offer the option B because it yield a higher net present value at the given rate.