Chapter 8.5, Problem 70E

a.

To determine

To write a recursive equation that shows how a_nis related to $a_{n-1}$

Answer to Problem 70E

  $a_n=1.08a_{n-1}+30,000$

Explanation of Solution

Given:

You plan to withdraw $30,000 at the beginning of each year for 20 years after you retire. Based on the type of investment you are making, you can expect to earn an annual return of 8% on sour savings after you retire.

Calculation:

The recursive rule for sequence $a_n$ .

  $a_1=3000$

  $a_n=1.08a_{n-1}+30,000$

b.

To determine

To find $a_0$ , the minimum amount of money you should have in your account when you retire

Answer to Problem 70E

  $a_{20}=1372859$

Explanation of Solution

Given:

You plan to withdraw $30,000 at the beginning of each year for 20 years after you retire. Based on the type of investment you are making, you can expect to earn an annual return of 8% on sour savings after you retire.

Calculation:

The following is the recursive rule-

  $\begin{array}{l}{a}_n=1.08a_{n-1}+30,000\\ a_{20}=1.08a_{19}+30,000\\ a_{20}=1372859\end{array}$