Homework #$3-$ Retirement Problems

$1-$You deposit $$5,000$ per year at the end of each of the next $25$ years into an account that pays $8\%$ compounded annually. How much could you withdraw at the end of each of the $20$ years following your last deposit if all withdrawals are the same dollar amount? $($The first withdrawal is made at the end of the first year in the $20-$year period.$)$

$2-$Cindy wants $$2\mathrm{.}5$ million for her retirement at age $65.$ Cindy is $25$ years old today and plans to deposit equal amounts each year starting on her ${26}^{th}$ birthday and ending on her ${65}^{th}$ birthday. If her investments earn $6\%$ per year, how much must each deposit be$?$

$3-$Suppose you want to retire when you reach age $70,$ at that time you want to have $$1,000,000$ accumulated in your retirement account. Now your $25$ years old, how much you have to save equally, at the end of each year, in order to reach your retirement goal if the account earns $5\%$ compounded interest?

$4-$You deposit $$3,000$ per year at the end of each of the next $30$ years into an account that pays $7\%$ compounded annually towards your retirement. Once you retire, you will withdraw your retirement savings in $15$ annual end$-$of year installments. If the accumulated money can earn an interest $4\%,$ how much you will be able to withdraw annually?

$5-$You want to deposit an equal amount of money every year at the end of each of the next $25$ years into an account that pays $7\%$ annually compounded interest, in order to be able to retire comfortably. During your retirement years, you want to have the ability to withdraw at the end of each of the $20$ years, the amount of $$40,000.$ During your retirement years, you will keep your money in an account that earns $4\%$ annually compounded interest. What should be your annual deposits during your working years?

$**$show steps and formulas$**$