Cost benefit analysis
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AN ENGINEER RECEIVED BY MAIL THE PROMOTION SHOWN BELOW FROM A LIFE INSURANCE COMPANY.HE HAS A NEW BORN CHILD AND WOULD LIKE TO INSURE THE CHILD,BUT DOES NOT KNOW THE OPTIMUM CHILD AGE AND THE BEST COVERAGE AMOUNT HE SHOULD SIGN UP FOR. HE NOTICES THAT THE MONTHLY PREMIUM STAYS THE SAME FOR EACH AGE GROUP SO THAT IT COULD BE LESS EXPENSIVE IF HE WAITED TILL THE CHILD WAS NEAR 7,15,21,OR 25 YEARS OLD. HE ALSO NOTICES THAT LOWER INSURANCE RATES ARE FOR THE YOUNGER CHILDREN WHO WOULD END UP PAYING SMALLER PREMIUMS BUT FOR LONGER PERIODS. HE NEEDS TO DECIDE ON THE BEST DEAL WHICH NATURALLY DEPENDS ON A VARIETY OF ASSUMPTIONS WITH REGARD TO THE INTEREST RATE, CHILD'S LIFE EXPECTANCY AND INFLATION RATE,ETC. WHICH PLAN WOULD YOU ADVISE HIM TO PURCHASE AND AT WHAT AGE OF THE CHILD.
AGE 0-7
$5000.00 COVERAGE- $2.43 A MONTH
$10000.00 COVERAGE- $4.10 A MONTH
$15000.00 COVERAGE- $5.78 A MONTH
$20000.00 COVERAGE- $7.45 A MONTH
AGE 8-15
$5000.00 COVERAGE $3.24 A MONTH
$10000.00 COVERAGE $5.56 A MONTH
$15000.00 COVERAGE $7.88 A MONTH
$20000.00 COVERAGE $10.21 A MONTH
AGE 16-21
$5000.00 COVERAGE $4.05 A MONTH
$10000.00 COVERAGE $6.89 A MONTH
$15000.00 COVERAGE $9.72 A MONTH
$20000.00 COVERAGE $12.55 A MONTH
AGE 22-25
$5000.00 COVERAGE $4.59 A MONTH
$10000.00 COVERAGE $7.95 A MONTH
$15000.00 COVERAGE $11.31 A MONTH
$20000.00 COVERAGE $14.67 A MONTH
PAY ONLY $1 FOR THE FIRST 3 MONTHS FOR UP TO $20000.00 LIFE INSURANCE COVERAGE
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Solution Summary
Cost benefit analysis is depicted for purchasing life insurance.
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please refer to the attachment
In this problem the benefit (coverage) that he can get is always the future value (end of life), we should find the future value of the total premium for each age group. And then compare it to the benefit that he can get. Then chose the best option.
Let's assume that the child can live "m=603" months and the MONTHLY COMPOUND interest rate stays at "r=1%" all the time. (actually you can put in any figure, but will yield the same result)
Then we can calculate the future value of the total premium for each age group using the ...
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