Question

You are 43 years old today and want to plan for retirement at age 65. You want to set aside an equal amount every year from now to retirement. You expect to live to age 95 and want to withdraw a fixed amount each year during retirement that at age 65 will have the same purchasing power as $98,093 has today. You plan on withdrawing the money starting the day you retire. You have not saved any money for retirement. Inflation is assumed to be 4.0% in the future. You expect to earn an 8.5% return on your investments in the future. How much do you need to save each year until retirement to meet your goal?

Answer #1

Retirement Annuity is required from the beginning of Year 65,

So, from Year 43(end) to 65(beginning),

Number of years = 21 years

Inflation Rate = 4%

Amount of Fixed Annuity payment required per year =
98093(1.04)^{21} = $223,531.20

Retirement payment is required from age 65 to 95,

Time Period = 31 years

Present Value of Annuity Due = P + P[(1 -
(1+r)^{-(n-1)})/r]

Present Value of Annuity Due = $2,625,786.09

Calculating Fixed Payment required from Year 43 to Year 65,

Time Period = 22 years,

Present Value = 0

Future Value = $2,625,786.09

Interest Rate = 8.50%

Using TVM Calculation,

PMT = FV(r/(1+r)((1+r)^{n} - 1))

PMT = $40,993.55

So,

**Payment Required from Year 43 to Year 65 =
$40,993.55**

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