Question

Bob is considering purchasing a two-year endowment policy with a $1,000 face amount at the beginning of his 50. The probability of Bob dying between 50 and 51 is 0.00550, and that between 51 and 52 is 0.00611. The annual interest rate is 6 percent.

(1) Calculate the net level premium for this two-year endowment policy.
(2) Show that this premium is just sufficient to fund benefits over the two years at the assumed interested and mortality rates.
(3) Ignoring expenses, what would the policy’s cash value equal after one year? (Round to two decimal places when calculating your answer.)

Answer 1

1) Solution: Net level premium = $453.87

Working:

[Face value x (1 - Mortality rate 1) * (1 - Mortatility rate2)] / (1 + Interest rate)^2

Putting values:

[1000 x (1-0.00550) x (1-0.00611)] / [(1.06) ^2]

= 988.424/1.1236

= 879.63

Now; P + P x (1-mortatility rate1) / (1+r) = 879.63

P + Px(1-0.00550) / 1.06 = 879.63

P + 0.93821 = 879.63

This gives P = 453.87

Net level premium = $453.87

2) FV = Premium + premium (1+ Rate of interest) x (1-0.00550)

= $453.87 + $453.87(1+0.06) x 0.9945

= $932.33

Thus the the net level premium is insufficient to fund benefits because face value is less than $1,000

3) Cash value after one year: Face value x (1 - Mortality rate 1) (1 - Mortality rate 2) / (1+ Rate of interest)

= [1000 (1 - 0.00550) (1 - 0.00611)] / 1.06

= $932.47