Question

An insurance company is considering the introduction of an investment-only product that provides a claim based on the accumulated value of premiums paid by a policyholder. Policyholders would pay annual premiums of X at Year 0, 1, 2, ..., n -1 and would receive a claim equal to the accumulated value of the premium payments at Year n . Unless told otherwise, for the following questions use an interest rate of 4% per annum and assume that n=25. Assume also that, for the moment, and until told otherwise, policyholders do not die during the 25 year policy period.

Question 3

A policyholder is wishing to receive a claim payment of $300,000. Calculate the value of the premium payment X , that will provide this claim payment.

Question 4

All other things remaining equal, what impact would a value of n= 30 instead of n= 25 have on
the calculated value of X in Question 3 for a claim payment of $300,000?

A) X is higher when n =30 compared to n =25

B) X is the unchanged when n= 30 compared to n =25

C) X is lower when n= 30 compared to n =25

NOTE:(I put tow Questions b.c it's related )

Answer 1

This a form of annuity.

Information given:

FV = $300,000

Time = 25

Interest = 4% per annum

Formula:

FV = Sum of FV of all payments

300,000 = PMT ( (1+0.04)^25 + (1+0.04)^24.... + (1+0.04) )

PMT = 300,000 / ( (1+0.04)^25 + (1+0.04)^24.... + (1+0.04) )

Solving using excel:

Thus the payments to be made are 6926.5$

300000 FV Rate 1 2 3 1.0816 1.125 4 5 6 7 8 9 1.17 1.217 1.265 1.316 1.369 1.423 10 11 1.48 1.539 12 13 14 15 16 17 18 19 20 21 1.601 1.665 1.732 1.801 1.873 1.948 2.026 2.107 2.191 2.279 22 23 24 25 2.37 2.465 2.563 2.666 1.04 Sum 43.312 Payment 6926.5

Question 4.

If everything else is constant and n= 30 instead of 25,

the payments would be as follows:

FV = Sum of FV of all payments

300,000 = PMT ( (1+0.04)^30 + (1+0.04)^29.... + (1+0.04) )

PMT = 300,000 / ( (1+0.04)^30 + (1+0.04)^29.... + (1+0.04) )

Solving using excel same as above,

PMT = 300,000 / 58.328

PMT = 5143.3$

This is lesser than the payment for n = 25 years

Thus answer - c) X is lower when n=30 compared to n=25