The question is asking to find X the answer is 461.82 Here is some of the textbo

Question

The question is asking to find X

the answer is 461.82

Here is some of the textbook to help understand.

$-36. Edgar was entitled to a monthly life annuity of 400 at age 65, but died on the day before the first payment was due. A death benefit. equal in value to half the value of the annuity, was payable to his beneficiary. Edgar's beneficiary is his girlfriend Linda, aged 22 The benefit is a 48-month temporary life annuity, commencing immediately, of X per month. Find X if D65 = 100, Mes = 900, Do = 2500, N22 = 53,000, D26-1950, and N26 = 43,500.

Explanation / Answer

Present value of the annuity is

a65'=[N65-(D65/2)]/D65+11/24=(900-50)/100 + (11/24)=8.96

PV of the net single premium= 400*12*a65'=400*12*8.96=43000

GIven Linda is now entitled to half the value of annuity=21500

which is to be paid in 48months monthly by an immediate temporary life annuity

a22:4(12) = (N22-N26)/D22 + (11/24)[1-D26/D22] = 21500= 3.90

Therefore X*12* 3.90=21500 =>X=21500/(12*3.9)=459.40

therefore X = 459.40

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