Assume that you inherited $$100,000$ from your grandparents, today. You have exactly $20$ years to retire and you decided to put the entire amount into $20$ years, $4\%$ annual interest annuity.

$1)(10$ pts$)$ Assuming you did not deposit any additional amount into this account, compute your account balance by the time you retire, using the annuity calculator. Then, compute the same using a scientific calculator $($not a financial one$)$ using the appropriate formulas from the textbook and show your calculations. $($Make sure the amounts are the same!$)$

$2)(10$ pts$)$ Now assume that in addition to this initial $$100,000,$ you also contributed $$500$ at the end of each month until you retire. Compute your retirement account balance using the annuity calculator. Highlight the end balance, total principal, and total interest.

$3)(30$ pts$)$ Please use the formulas with the periodic rate inserted using $6-$digit sensitivity$.$ Clearly mark your answers to specific sections as $3($A$),3($B$),$ and $3($C$).$

$3($A$)(10$ pts$)$ Explain how the periodic rate is obtained. Show the periodic rate using six$-$digit sensitivity$.(0\mathrm{.}000000)$

$3($B$)(10$ pts$)$ Using the relevant formulas from the textbook and a scientific calculator, show the values of the interest from monthly $$500$ additions, and total return$/$interest earned.

$3($C$)(10$ pts$)$ Please explain how the End Balance appearing in $(2)$ above is computed using all four components of the END Balance: $1)$ The inherited amount, $2)$ The amount of interest earned by the inherited amount, $3)$ The total monthly editions of $$500$ per month deposited at the end of the months, $4)$ The interest earned from the monthly $$500$ additional end$-$of$-$the$-$month deposits. Do not use tautological forms such as end balance $=$ total principal $+$ total interest.

$4)(30$ pts$)$ Assume that the contributions were made at the beginning of each month. Clearly mark your answers to specific sections as $4($A$),4($B$),$ and $4($C$).$

$4($A$)(10$ pts$)$ Using the relevant formulas from the textbook and a scientific calculator, show the amount of interest earned from the initial principal.

$4($B$)(10$ pts$)$ Using the relevant formulas from the textbook and a scientific calculator, show the total amount of interest earned from monthly $$500$ additions.

$4($C$)(10$ pts$)$ Please explain how the End Balance is computed using all four components of the End Balance: $1)$ The inherited amount, $2)$ Interest earned by the inherited amount, $3)$ The total monthly editions of $$500$ per month deposited at the end of each month, $4)$ The interest earned from the end$-$of$-$month $$500$ additional deposits. Do not use tautological forms such as end balance $=$ total principal $+$ total interest.

$5)(20$ pts$)$ Now, look at the first row of the $$Annual Schedule$$ table $[$continue from $(4)]$ provided by the calculator $($just under the graph$)$: Copy the last three values $($Addition$,$ Return, Ending Balance$).($The values as of the end of the first year.$)$

Please show how the "Return" amount is computed using an appropriate formula. Do not use a financial calculator and do not use tautological forms such as Return $=$ Ending Balance $-$ Addition.

Interest