APR is an annualized rate, meaning the yield if the periodic interest is compounded for an entire year. To convert it to a monthly rate, use a slightly different formula;
r = (APY+1)^(1/12) - 1
That gives a monthly rate of 0.1978%, which if used in the FV formula gives exactly the $194,410.60
You don't need to put it towards anything in particular. There's no requirement that a pot of money has to have a label on it saying what you're going to use it for.
If you invest it in a diversified investment fund, it can sit there until you decide what you need it for. That could be a car, a deposit on a house, or it could stay there until you retire.