A special account pays $4\%$ nominal interest compounded every $6$ months. What $is$ the

effective annual rate?

After graduating college, you receive $$50,000$ and decide $to$ put $itin$ a high yield saving

account. The account earns $3\%$ every $6$ months.

$(a)$ What are the nominal and effective annual interest rate?

$(b)If$ you leave your initial investment $in$ the account without any withdrawals, what

would you expect the value $of$ the account $tobe$ after $5$ years?

A car may $be$ purchased with $a$ $$9,000$ down payment now and $36$ monthly payments

$of$ $$900.If$ the $(annual)$ interest rate $is8\%$ compounded monthly, what $is$ the price $of$

the car?

The cash flows below are equal. Both are calculated $at$ a rate $of7\%$ compounded

annually. What $is$ the uniform annuity that makes these cash flous equal?

A debt $of$ $$8,000on$ a credit card can $be$ repaid, with $(annual)$ interest $of8\%,by$ the

following payments.

The payment $at$ the end $of$ the fifth year $is$ shown $asx.$ How much $isx?$

A young engineer wishes $to$ become a millionaire $by$ the time $beis40$ years old. $He$

believes that $by$ careful investment $he$ can obtain $a20\%(annual)$ rate $of$ return. $He$

plans $to$ add a uniform sum $of$ moncy $to$ his investment program each year, beginning

$on$ his $20th$ birthday and continuing through his $39th$ birthday. How much moncy must

the engineer set aside $in$ this project each year?

Compute the present value for the following cash flows with $r=10\%$ :

$(a)$