You are considering having a Honda hybrid car for three years during your working holiday in Australia. The car costs $$49,000.$ You can either lease $($i$.$e$.$ an agreement by which you pay periodic fees to use the asset, but you do not own the asset$)$ the car or purchase the car. The car dealer has the following arrangement for you:

Option $1($Leasing the Car$)$: You pay $$5,100$ today and $$545$ at the end of each month for the next three years, last payment occurs at the end of year $3.$

Option $2($Purchasing the Car$)$: You pay $$49,000$ now for the car in one lump sum, but you will be able to resell the car for $$32,000$ at the end of year $3.$

a$)$ Draw the Timeline to illustrate the cash flow for Option $(1)$ and Option $(2).(4$ marks$)$

b$)$ Given the relevant interest rate is $5\mathrm{.}3\%$ compounded monthly, by computing the PV should you lease or purchase the car?

$(9$ marks$)$