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
a. None of the options are correct.
b. You should accept the $200,000 lump sum because the monthly payments are only worth $189,311 to you today.
c. You should accept the monthly payments because they are worth $209,414 to you.
d. You should accept the $200,000 lump sum because the monthly payments are only worth $16,057 to you today.
e. You should accept the $200,000 lump sum because the monthly payments are only worth $195,413 to you today.
f. You should accept the monthly payments because they are worth $336,000 to you.

Answer 1

After calculating the present value of the monthly payments (using the formula for present value of annuity), it is determined that the option to accept the monthly payments is financially better as they are worth approximately $209,414 today, compared to the $200,000 lump sum offer.

Step-by-step explanation:

The student is faced with the decision of choosing between a $200,000 lump sum payment today or monthly payments of $1,400 for 20 years when they can earn a 6% annual rate, compounded monthly on their investments. To determine which option is financially better, we need to calculate the present value of the annuity (monthly payments) and compare it to the lump sum offered.

To find the present value of the monthly payments, we can use the present value of annuity formula: PV = Pmt * [(1 - (1 + r)^(-n))/r], where Pmt is the monthly payment, r is the monthly interest rate (annual rate divided by 12), and n is the total number of payments. Since the monthly interest rate is 0.06/12 and there are 240 payments (20 years * 12 months), the equation becomes: PV = 1400 * [(1 - (1 + 0.005)^(-240))/0.005]. After calculating, the present value of the monthly payments is approximately $209,414.

Since the present value of the monthly payments is greater than the $200,000 lump sum being offered, the best financial choice would be option c, to accept the monthly payments since they are worth $209,414 to you today.