$1.$ You are buying a car. You have two options.

a$.$ Put $5000$ down and borrow the rest. Payments on this option are $4000/$year for $3$ years. $($one payment per year at the end of the year$)$

b$.$ Put zero down. Payments on this option are $7000/$year for $3$ years. $($one payment per year at the end of the year$)$

DISCOUNT Factor is $4\%$ in both cases. $($this is the interest rate you could earn on savings$).$ WRITE out the formula for finding the present value of each option.

i$.$ Option $1$

ii$.$ Option $2$

c$.$ Which option should you choose? $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$2.$ You receive a $$900$ stimulus check from the government. It allows you to either buy a discount bond and in $2$ years it pays you back $$1000$; or$,$ you can use the check to pay down your credit card debt. The rate on your credit card is $15\%.$

a$.$ What is the most that you should pay for the discount bond?

$3.$ You buy a $10-$year discount bond today for $$1100.$ It has a face value of $$1000.$

a$.$ What is the YTM$?$

b$.$ If interest rates on similar bonds are $5\%$ at the end of the fifth year and you decide to sell it$,$ how much will you be able to sell it for?

c$.$ What is your rate of return on this stream of payments?