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Your sister turned 35 today, and she is planning to save $7,000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund that's expected to provide a return of 7.5% per year. She plans to retire 30 years from today, when she turns 65, and she expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can she spend each year after she retires

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Tundexi

Answer:

$64,932

Explanation:

Calculate the accumulated sum after 30 years by using below formula:

S = R[(1+i)^n - 1]/i  

Where

S = the accumulated sum

R = the yearly deposit

i = the decimal interest rate per year

n = the total count of deposits

This results in a sum accumulation of $723,796.

Now calculate annual payout for a 25-year old annuity by using below formula:

R = Pi/[1 - (1+i)^(-n)]  

This gives the PMT of $64,932.  

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Answer:

She can spend $64,932  each year after she retires

Explanation:

Future Value of deposits = 7000[[tex](1+i)^{30}[/tex] + [tex](1+i)^{29}[/tex] + ... + [tex](1+i)^{1}[/tex]] , where i = 7.5%

= $778,080

The value of her fund at retirement is $778,080.

Let the annual drawing be of amount Z.

The Present Value of drawings should equal the size of fund.

$778,080 = Z[[tex](1+i)^{-0} +(1+i)^{-1} +...+ (1+i)^{-24}[/tex]] , where i = 7.5%

$778,080 = Z*11.98

Z = $64,932

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