Your MacBook Pro broke down unexpectedly. You can purchase a new laptop for $3,000$ euro. The alternative is to lease it and pay $75$ euro at the end of each month for a period of four years. The appropriate interest rate is a $5\%$ annual percentage rate $($APR$)$ with semi$-$annual compounding. Intuitively, you feel the lease is more expensive than a direct purchase. How much more expensive is the lease versus a direct cash buy of the laptop? Which answer comes closest?

Your answer is correct

$10\mathrm{.}0\%$ more expensive

$5\mathrm{.}5\%$ more expensive

$7\mathrm{.}0\%$ more expensive

$8\mathrm{.}5\%$ more expensive