YPart $1$: Finance $1$

You can score $22$ pts$.$

$($a$)(2$ points$)$ If the future value at time $T=5$ years is $$2000$ and the effective interest rate is $2\%$ per

year based on monthly compounding, then what is the corresponding present value? $($round to two

decimals$)$

$($b$)(4$ points$)$ You are considering the purchase of a new race bike. Your old race bike has only $3$

months of life remaining. The value of the current bike is $250$$$.$ The new bike would last for

$2$ years. Assuming that costs will remain constant and that the yearly nominal interest rate is

$5\%,$ what value would you assign to the new bike? $[$Hint: monthly compouding.$]($round to zero

decimals$)$

$($c$)(2$ points$)$ Assume that some countries have a higher chance of defaulting than others. What do

you expect to happen to the bond prices and yield$-$to$-$maturities issued by those governments that $($d$)(3$ points$)$ What is the $5-$year interest rate if a coupon bond with a face value of $100,$ a coupon

rate of $5\%$ and a maturity of $5$ years is selling for $93$ and another coupon bond with a face value

of $100,$ a coupon rate of $8\%$ and a maturity of $5$ years is selling for $95?($round to two decimals$)$ou are considering the purchase of a new race bike. Your old race bike has only $3$months of life remaining. The value of the current bike is $250$$$.$ The new bike would last for$2$ years. Assuming that costs will remain constant and that the yearly nominal interest rate is$5\%,$ what value would you assign to the new bike? $[$Hint: monthly compouding.$]($round to zerodecimals$)$