Peter and Marcia, both age 34, can each pay $650 a year each on life insurance for themselves. About how much is the face value of the largest combination of policies they can buy?

Question

Peter and Marcia, both age 34, can each pay $650 a year each on life insurance for themselves.  About how much is the face value of the largest combination of policies they can buy?
For age 34, a 10-year term for male is 1.45 and for female is 1.24. A 20-year term for male is 1.89 and female is 1.46.
a.
$1,945,000
b.
$972,000
c.
$789,000
d.
$806,000

GPT 3.5 · Answer

To find the face value of the largest combination of policies they can buy, we need to figure out how much insurance each of them can buy with their annual premium of $650.

For Peter, the 10-year term policy for males at age 34 costs 1.45 times the annual premium. Therefore, Peter's annual premium can buy $650 * 1.45 = $942.50 worth of insurance.

For Marcia, the 10-year term policy for females at age 34 costs 1.24 times the annual premium. Therefore, Marcia's annual premium can buy $650 * 1.24 = $806 worth of insurance.

Now, we need to calculate the total face value they can get together. Since they can each get insurance worth $942.50 and $806 with their annual premiums, the largest combination of policies they can buy is $942.50 + $806 = $1748.50.

However, this is the total face value they can get for one year only. To find the total face value for a longer period, we need to multiply this amount by the number of years of the term policy they want.

Let's assume they both want to get a 20-year term policy. The 20-year term policy for males at age 34 costs 1.89 times the annual premium, so Peter could get $942.50 * 1.89 = $1781.925 worth of insurance for 20 years.

For females, the 20-year term policy at age 34 costs 1.46 times the annual premium. Therefore, Marcia could get $806 * 1.46 = $1175.36 worth of insurance for 20 years.

Multiplying these amounts by the number of years, we have $1781.925 * 20 = $35,638.50 for Peter and $1175.36 * 20 = $23,507.2 for Marcia.

Adding these two amounts together, we have $35,638.50 + $23,507.2 = $59,145.70.

Therefore, the face value of the largest combination of policies they can buy is about $59,145. The closest option to this amount is d. $806,000, so the answer is d. $806,000.