David purchased a $100,000 participating whole life policy. The annual premium is $2,280. Projected dividends for the first 20 years are $15,624. The cash value after 20 years will be $35,260. If the premiums were invested at 5 percent for 20 years, the premiums would grow to $79,156. If the dividends were accumulated at 5 percent for 20 years, they would grow to be $24,400. The amount to which $1 deposited annually will accumulate in 20 years at 5 percent is $34.719. Based on this information, what is the net payment cost per thousand per year of David's policy over the 20-year period?

Question

David purchased a $100,000 participating whole life policy. The annual premium is $2,280. Projected dividends for the first 20 years are $15,624. The cash value after 20 years will be $35,260. If the premiums were invested at 5 percent for 20 years, the premiums would grow to $79,156. If the dividends were accumulated at 5 percent for 20 years, they would grow to be $24,400. The amount to which $1 deposited annually will accumulate in 20 years at 5 percent is $34.719. Based on this information, what is the net payment cost per thousand per year of David's policy over the 20-year period?

Answer 1

To calculate the net payment cost per thousand per year of David's policy over the 20-year period, we need to consider the premiums paid, the dividends received, the cash value, and the growth of premiums and dividends if invested at 5 percent for 20 years.

1. Calculate the total premiums paid over 20 years:
Annual premium: $2,280
Total premiums paid: $2,280 * 20 = $45,600

2. Calculate the total dividends received over 20 years:
Projected dividends for the first 20 years: $15,624

3. Calculate the growth of premiums if invested at 5 percent for 20 years:
Initial premium: $2,280
Growth rate: 5 percent
Period: 20 years
Future value of premiums = $2,280 * (1 + 0.05)^20 = $79,156

4. Calculate the growth of dividends if accumulated at 5 percent for 20 years:
Initial dividend: $15,624
Growth rate: 5 percent
Period: 20 years
Future value of dividends = $15,624 * (1 + 0.05)^20 = $24,400

5. Calculate the net payment cost per thousand per year:
Net payment cost = (Total premiums - Total dividends + Future value of premiums - Future value of dividends) / (Policy amount / 1,000)

Total premiums = $45,600
Total dividends = $15,624
Future value of premiums = $79,156
Future value of dividends = $24,400
Policy amount = $100,000

Net payment cost = ($45,600 - $15,624 + $79,156 - $24,400) / ($100,000 / 1,000)

Simplifying the equation:
Net payment cost = ($84,732) / (100)
Net payment cost = $847.32 per thousand per year

Therefore, the net payment cost per thousand per year of David's policy over the 20-year period is $847.32

$5.17

To calculate the net payment cost per thousand per year of David's policy over the 20-year period, we need to consider the premiums paid, the dividends received, the cash value, and the growth of premiums and dividends if invested at 5 percent for 20 years.