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4. After retirement, you expect to live for 25 years. You would like to have $75,000...

4. After retirement, you expect to live for 25 years. You would like to have $75,000 income each year. How much should you have saved in your retirement account to receive this income, if the annual interest rate is 9 % per year? (Assume that the payments start on the day of your retirement.

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Answer #1
This can be solved using the Present value of annuity due formula
Present value of annuity due is = P+[P*(1-(1+r)^-(n-1))/r]
"P" is Annual income for each year = $ 75,000/.
"r" is Annual interest rate = 9%
"n" is No of years = 25
Present value of annuity due is = Savings
Present value is = 75000+[75000*(1-(1+0.09)^-(25-1))/0.09]
Present value is = 75000+[75000*9.706612]
Present value is = 75000+[727995.88]
Present value is = $ 802,995.88/.
Hence $ 802,996/. have saved in retirement account
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