The batteries alone would cost you more than $700 unless you only wanted to go that fast for about a minute. Nothing even remotely fitting that price that will go that fast, which is illegal under federal regs btw, on the horizon even.
You may be able to find a used electric scooter for that price though.
Electrics are usually more expensive than gas bikes and don't have as high speed. You could get close to 25mph with a Wilderness Energy 36 volt kit and add a battery for 48V, put it on a garage sale mountain bike. You could do that for less than $700.