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Paul "Plan Ahead" Parker Time Value of Money Problem

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Mr. Paul "Plan Ahead" Parker has come to you for some retirement planning advice. As a recent college graduate he knows the value of planning ahead (thus his nickname). He wants to know how much he should start putting aside each year so that he will have a sufficient nest egg with which to retire at the age of 65 (40 years away). He's just turned 25 and based on actuarial tables factoring in height, weight, diet, consumption habits, relative fitness, marital status, pet ownership, and genetic history he expects to live until the end of his 85th year, at which time he will promptly expire (20 years of retirement). Though he likes to live well now, Paul believes he can make it on a retirement salary of $35,000 per year.

This assumes he pays off his house before retirement, stops buying new computers every time they come out, and that his only dependent will be a small cat whose lifestyle will be rather modest. Further, he figures that during retirement, his money will be invested conservatively at about 5% per year. Before retirement, Paul sees no reason he shouldn't get the average 12% he usually gets. How much should Paul start saving each year to have the retirement he plans? If Paul procrastinates and starts saving for retirement at age 55 (10 years to retirement) what will his annual savings amount have to be?

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Since Paul needs an annuity of $35,000 for 20 years, we need to calculate the value of this annuity at the beginning of his retirement i.e. when he ...

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computation and formulas given

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