$3.$ Harold invested $$700$ at a $4\mathrm{.}5\%$ interest rate compounded annually. How long will it take for the investment to have a future value of approximately $$1400?.$

$4.$ Nick wants to purchase a new car that costs $$31000($all fees and taxes included$).$ He wants to pay the car off in $5$ years. The dealership gives him two options. He can either: Option $1$: get $$5200$ off the total price of the car, with a bank loan for the remainder at an interest rate of $7\mathrm{.}9\%$ per year, compounded monthly; or Option $2$: get no money off the price of the car with a loan from the car company at an interest rate of $1\mathrm{.}9\%$ per year compounded monthly.Determine:a$)$ the monthly payment for each option.$(8$ marks$)$b$)$ the difference in the monthly payment between the two options.