An investment account is worth $$1000$ on January $1,2020.$ X months before the end of $2020,$ the balance has increased by $$50x,$ and $$500$ is deposited into the account. At the end of $2020,$ the balance is $$2000.$ If the dollar$-$weighted rate of return for the year is $40\%,$ find the timeweighted rate of return. Show all work please. Not on excel.