Your retirement account guarantees a fixed rate of 8% per year paid yearly. You

Question

Your retirement account guarantees a fixed rate of 8% per year paid yearly. You start saving for retirement at age 30 with a target retirement age of 65 and dollar 0 in your saving account. Use first order difference equations to answer the following questions (all interests and payments are computed on a yearly basis). You set aside dollar 500 every month (or dollar 6000 a year). How much money will you have for your retirement? You want to retire with $500,000. How much should you save every year? You assume that your salary will increase 5% every year and so you decide your contribution should also increase by 5% even,' year. If your starting contribution is dollar 500 even,' month how much money will you have saved at retirement age? Assuming again that your contribution is increasing by 5% every year, what should your starting contribution be if if you want to reach dollar 500,000 by retirement age?

Explanation / Answer

At+1 = At + 6000(1+r), A0 = 0

a) Rearranging, At+1 - At = 6480

A1- A0 = 6480

A2 - A1 = 6480

A3 - A2 = 6480 and so on until A34

So Money at retirement = 6480 * 35 = $ 226, 800

b) 500,000 = 35* x * 1.08 or x = $13,227

c) Recurrence reation will change now as the contribution is no longer fixed

   At+1 = At + 6000(1.05)^t(1.08)

          = At + 6480*(1.05)t

Proceed similarly to solve parts c and d.

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