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(a) A financial planner recommends that you have accumulated $1.5 million by the time that you retire in 30 years. If you can earn

 

(a) A financial planner recommends that you have accumulated $1.5 million by the time that you retire in 30 years. If you can earn an annual rate of return of 7%, how much must you invest for each of the next 30 years to achieve this goal? (b) If you were to save $12,000 at the end of each of your 30 working years earning 7% per year, how much would you have accumulated by the time you retire? (c) If you have $2 million at the beginning of your retirement period and can earn 7% per year, what size equal annual withdrawals could you make during your 20 years of retirement that would leave you with a zero balance? (d) If you want to make equal annual withdrawals of $150,000 during your 20-year retirement period and can earn 7% per year, how much must you have accumulated by the beginning of your retirement?

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ANSWER a To accumulate 15 million in 30 years with an annual rate of return of 7 we can use the formula for the future value of an annuity FV PMT x 1 ... blur-text-image

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