$(4)$ A young couple that recently had their third child decide to purchase a new van. They make a down payment of $$10,000$ and finance the remaining $$22,000$ to purchase a $2010$ Toyota Sienna. They arrange financing with their local financial institution and arrange an annual interest rate of $5\mathrm{.}2\%$ compounded monthly. They decide to make monthly payments of $$400.$ How long will it take for them to pay off the van?