1.) I am now 45 years old and I want to retire in 15 years when I am 60. When I
ID: 2713342 • Letter: 1
Question
1.)
I am now 45 years old and I want to retire in 15 years when I am 60. When I retire, I would like to collect $80,000 per year for the estimated 24 years that I will live. I would like my first payment of $80,000 to be given to me at the end of my first retirement year. If my insurance company has a product like that that I can buy now, and that will earn 7% interest compounded annually, what should I expect to pay for this financial product?
2.)
Your insurance agent tells you the current price of the following policy is $94,372.
Time until annuity benefit begin
15 years
Amount of monthly annuity benefit( to be received at the end of the first month after the benefit period begins)
Annual rate of return promised over entire period
12.0 %
If you purchase this policy, how many years will your benefits last once they start?
3.)
An insurance company’s projected loss ratio is 77.50 percent and it’s loss adjustment expense ratio is 12.90 percent. It estimates that commission payments and dividends to policyholders will add another 16 percent. What is the minimum yield on investments required in order to maintain a positive operating ratio?
4.)
A property-casualty insurer brings in $6.25 million in premiums on its homeowners MP (multiple peril) line of insurance. The line’s losses amount to $4,343,750, expenses are $1,593,750, and dividends are $156,250. The insurer earns $218,750 from the investment of its premiums. Calculate the line’s loss ratio, expense ratio, dividend ratio, combined ratio, investment ratio, operating ratio, and overall profitability.
1.)
I am now 45 years old and I want to retire in 15 years when I am 60. When I retire, I would like to collect $80,000 per year for the estimated 24 years that I will live. I would like my first payment of $80,000 to be given to me at the end of my first retirement year. If my insurance company has a product like that that I can buy now, and that will earn 7% interest compounded annually, what should I expect to pay for this financial product?
Explanation / Answer
Q1)
Amount Required at the time of Retirement = Annual Withdrawl required*(1-(1+r)^-n)/r
Amount Required at the time of Retirement = 80000*(1-(1+7%)^-24)/7%
Amount Required at the time of Retirement = $ 917,546.72
Amount should I expect to pay for this financial product today = Amount Required at the time of Retirement /(1+r)^n
Amount should I expect to pay for this financial product today = 917546.72/(1+7%)^15
Amount should I expect to pay for this financial product today = $ 332,561.16
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