An insurance company is offering a new policy to its customers. Such a policy is

Question

An insurance company is offering a new policy to its customers. Such a policy is typically bought by parents or grandparents at the time the baby is born. The details of the policy are shown below. Assume the child is born today.

       You pay premiums as follows: Today, at the time of birth of the child, you pay $500. First birthday $600, Second birthday $700, Third birthday $800, Fourth birthday $900, Fifth birthday $1,000 and Sixth birthday $1,100. There are no payments due after the child’s sixth birthday.   When the child reaches age of 65, he or she receives $500,000. If the relevant interest rate is 9% CQ for the first 6 years and 7% CM for all subsequent years, is the policy worth buying?

Explanation / Answer

**If you invest $ 500 today, it will compounded wit interest rate of 9 % for 6 years and you will get 838.55 at the end of 6 th year,

similarly for 2 birthday and so on

Now you will receive cash at the age of 65 so remaining years to your birthday after 6 years = 65 - 6 = 59 years

so the value of cash flow 7045.14 at the end of 65 years=

7045.14 ( 1+.07)^59

7045.14 * 54.15554

$381,533.35

since you receiving $ 500,000 for your investment it is worth of taking the policy that cost you only $ 381,533.35

generating a gain og $118,466.65

cash flow Future value of cash flow at the end of 6 year @ 9% future value (a*b) 500 (1.09)^6 838.55 600 (1.09)^5 923.17 700 (1.09)^4 988.11 800 (1.09)^3 1036.02 900 (1.09)^2 1069.29 1000 (1.09)^1 1090 1100 1 1100 value of cash deposited at the end of 6 year 7045.14

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