Question

You are the beneficiary of a life insurance policy. The insurance company informs you that you have two options for receiving the insurance proceeds. You can receive a lump sum of $200,000 today or receive payments of $1,400 a month for 20 years. You can earn a 6% annual rate on your money, compounded monthly. Which option should you take and why?

Multiple Choice
1) None of the options are correct.
2) You should accept the $200,000 lump sum because the monthly payments are only worth $189,311 to you today.
3) You should accept the monthly payments because they are worth $209,414 to you.
4) You should accept the $200,000 lump sum because the monthly payments are only worth $16,057 to you today.
5) You should accept the $200,000 lump sum because the monthly payments are only worth $195,413 to you today.
6) You should accept the monthly payments because they are worth $336,000 to you.

Answer 1

To determine which option is better, compare the present value of the lump sum and the present value of the monthly payments. The present value of the lump sum is $195,413, while the present value of the monthly payments is $209,414. Therefore, the correct option is to accept the monthly payments.

Step-by-step explanation:

To determine which option is better, we need to compare the present value of the lump sum and the present value of the monthly payments.

For the lump sum option, the present value can be calculated using the formula: PV = FV / (1 + r/n)^(n*t), where PV is the present value, FV is the future value, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

For the monthly payments option, the present value can be calculated as the sum of the present values of each monthly payment. Using the same formula, we can calculate the present value of each payment and then sum them up.

After performing the calculations, we find that the present value of the lump sum is $195,413, while the present value of the monthly payments is $209,414. Therefore, the correct option to choose is Option 3) You should accept the monthly payments because they are worth $209,414 to you.