Steven wishes to save for his retirement by depositing $2,000 at the beginning of each year for thirty years. Exactly one year after his last deposit, he wishes to begin making annual level withdrawals until he has made twenty withdrawals and used up the savings. Find the amount of each withdrawal if the effective interest rate is 3% during the first thirty years but only 2% after that.

Step-by-step explanation:

i = interest 3% for 30 years

This is a simple dynamical system for whom the the solutions are given as

putting values we get

S=2000[\frac{(1.03)^{30}-1}{0.03}](1.03)

= $98005.35

withdrawal of money takes place from one year after last payment

To determine the result we use the present value formula of an annuity date

we need to calculate R so putting the values and solving for R we get

R= $6542.2356

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.

a. she will receive a refund of $278.

step-by-step explanation: