Your client, a man, is currently 35 year old and he wants to retire when he is 6

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Your client, a man, is currently 35 year old and he wants to retire when he is 65 years old (exactly 30 years from now). He would like his retirement income to be equivalent to $6,000 per month, adjusted for inflation. You estimate the inflation rate for the next 30 years to average 3% annually. He anticipates purchasing a guaranteed retirement annuity from an insurance company the month before he retires (359 months from now). The insurance company will use the actuarial life expectancy table below to determine the cost of the annuity. As you can see, he is expected to live about 16 years (so, he should expect to purchase a 193 month annuity) following retirement. They will add a 4% premium to the pure premium calculated from their actuarial table. He has $25,000 in savings today that will be invested until he retires. Given a rate of return of 6% (annually but compounded monthly) for the foreseeable future for both your client and the insurance company, how much does he need to save each month (359 months) for the next 29 years and 11 months (first payment to be made in one month) if he is to afford to purchase the annuity contract? (Assume that you make the last monthly payment in 29 years and 11 months, the month before you receive your first monthly retirement payment.) What dollar amount will be needed per month at retirement age? (HINT: You want the equivalent to 6,000 per month when you retire; however, inflation will be 3% over the next 30 years! So you want to calculate the FV in 30 years.) FV.30years= OK, in part (1) you calculated the monthly dollar amount needed for retirement. Now you need to determine what the PV of this stream of retirement income will be (one month before retirement). HINT: This will be the PVA of the stream of monthly retirement income - from part (I) - for 193 months. Remember this PV is in the liiture when you are ready to retire.) PVA month359 = PVA 193 months= What will the price of this annuity? (HINT: This next step is easy - you need to determine what this annuity will cost. The figure you arrived at in part (2) Ls the pure premium. Now you need to increase this by the amount the insurance company adds to the pure premium.) Price =PVAmonth359x Premium= What is the future value of your client's savings in 359 months when he plans to retire? (HINT: Your client has savings - what will these be worth in the future?) FV359 months = What is the new total amount needed by month 359 when he plans to retire? (HINT: This is easy to calculate - it is the amount from (3) minus the figure determined in (4).) How much needs to be saved monthly so you will have sufficient savings to purchase this annuity from the insurance company? (HINT: You need to solve for the annuity amount. You know the FVA, the interest rate, number of periods.)

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