You deposit $12,000 annually into a life insurance fund for the next 40 years, a

Question

You deposit $12,000 annually into a life insurance fund for the next 40 years, after which you plan to retire.

What are the considerations when you are looking for a certain life insurance fund?

b. If the deposit is made at the beginning of the year and earn an interest of 7 percent, what will be the amount after the end of year 40?

c. You wish to receive annuities for the next 20 years (year 41 to 60). What is the annual payment you expect to receive at the beginning of the year if the interest is 7 percent in year 41 to 60?

d. Repeat step b and c with 8 percent interest and 6 percent interest and show the difference in terms of annual payment.

e. Would you personally invest into this kind of insurance fund? If not, what kind of investment are you interested in? Please explain why.

Explanation / Answer

b.) Amount at the end of 40 years = 12,000 x {(1+0.07)40 -1 )/0.07}x(1+0.07)

                                                  = 12,000x199.6351x1.07

                                                  = $2,563,314.84

c.) If the annuity is to be received for first 20 years post retirement, this will be calculated from present value of annuity due and equating it to the corpus available in that account.

P + Px{(1-(1+0.07)-20)0.07} = 2,563,314.84

P + Px10.5940 =2,563,314.84

P = 221,089.50

Hence, she can expect to receive $221,089.50 annually in the form of annuity at the start of each year for 20 years.

d.) Using 8% Rate of Interest

12,000 x {(1+0.08)40 -1 )/0.08}x(1+0.08) = P + Px{(1-(1+0.08)-20)0.08}

12,000 x 259.0565 x 1.08 = P + Px9.8181

P = 310,347.68

Difference in Annual Payment against 7% interest =310,347.68 - 221,089.50 = $289,258.18

Using 6% Rate of Interest

12,000 x {(1+0.06)40 -1 )/0.06}x(1+0.06) = P + Px{(1-(1+0.06)-20)0.06}

12,000 x 154.7620 x 1.06 = P + Px11.4699

P = 157,865.68

Difference in Annual Payment against 7% interest =221,089.50 - 157,865.68 =$63,223.82

e.) Yes, I would personally advise to invest in this kind of insurance fund as it will provide a secured source os funds post retirement when the options of income sources are limited. Moreover, disciplined savings each year is leading to build up of good corpus amount for future.

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