Question

An insurance company is offering a new policy to its customers. Typically the policy is bought by a parent or grandparent for a child at the child’s birth. The details of the policy are as follows: The purchaser (say, the parent) makes the following six payments to the insurance company:

First birthday $400

Second birthday $500

Third birthday $ 600

Fourth birthday $700

Fifth birthday $800

Sixth birthday $900

 

After the child’s sixth birthday, no more payments are made. When the child reaches age 65, he or she receives $250,000. If the relevant interest rate is 11 percent for the first six years and 7 percent for all subsequent years, is the policy worth buying? (explain with a equation as well)

 

Answer 1

THIS IS A CASE OF FUTURE VALUE OF SUM

AS MONEY IS RECEIVED AT THE END OF 65 YEARS, WE HAVE TO CALCULATE FUTURE VALUE OF ALL SUMS FOR 65 YEARS

AS FIRST PAYMENT IS MADE AT THE END OF 1ST YEAR, 11% RATE WILL BE AVAILABLE FOR ONLY 5 YEARS

FIRST = 400 X FVIF 11% FOR 5 YEARS X FVIF 7% FOR 59 YEARS

SECOND = 500 X FVIF 11% FOR 4 YEARS X FVIF 7% FOR 59 YEARS

THIRD = 600 X FVIF 11% FOR 3 YEARS X FVIF 7% FOR 59 YEARS

FOURTH = 700 X FVIF 11% FOR 2 YEARS X FVIF 7% FOR 59 YEARS

FIFTH = 800 X FVIF 11% FOR 1 YEARS X FVIF 7% FOR 59 YEARS

SIXTH = 900 X FVIF 7% FOR 59 YEARS

FIRST = 400 X 1.6851 X 54.1555 = 36502.97

SECOND = 500 X 1.5181 X 54.1555 = 41106.73

THIRD = 600 X 1.3676 X 54.1555 = 44437.84

FOURTH = 700 X 1.2321 X 54.1555 = 46707.49

FIFTH = 800 X 1.11 X 54.1555 = 48090.01

SIXTH = 900 X 54.1555 = 48740

SO TOTAL AMOUNT AT THE END OF 65 YEARS = 36502.97 + 41106.73 + 44437.84 + 46707.49 + 48090.01 + 48740 = $265585.04

AND INSURANCE COMPANY PAYS $250000

SO POLICY NOT WORTH BUYING (ANSWER)