You$$re trying to save to buy a vacation home that will cost $$650,000.$ You have $$150,000$ today that can be invested at your bank. The bank pays $4\mathrm{.}2$ percent annual interest on its accounts. How long will it be before you have enough to buy the house $($assuming the cost of the house remains unchanged$)?$ After calculating the number of years, you determine that you do not want to wait that long. Instead, you believe you can invest a sum of money in a fund that returns an annual rate of $11\%.$ You want to buy this home in $10$ years. How much must you invest today have enough funds to buy the house?