The market value of that home may have doubled to $800,000. But because the down payment locked in a pre-determined price, the buyer pays $400,000. Now, in an alternate scenario, say the zoning approval doesn’t come through until year four. This is one year past the expiration of this option. Now the home buyer must pay the market price because the contract has expired. In either case, the developer keeps the original $20,000 collected.
When buying a call option, the strike price of an option for a stock, for example, will be determined based on the current price of that stock. For example, if a share of a given stock (like Amazon (AMZN) ) is $1,748, any strike price (price of the call option) that is above that share price is considered to be "out of the money." Conversely, if the strike price is under the current share price of the stock, it's considered "in the money." 
A call option is a contract that gives the investor the right to buy a certain amount of shares (typically 100 per contract) of a certain security or commodity at a specified price over a certain amount of time. For example, a call option would allow a trader to buy a certain amount of shares of either stocks, bonds, or even other instruments like ETFs or indexes at a future time (by the expiration of the contract). 

The purchase of a call option is a long position, a bet that the underlying futures price will move higher. For example, if one expects corn futures to move higher, they might buy a corn call option. The purchase of a put option is a short position, a bet that the underlying futures price will move lower. For example, if one expects soybean futures to move lower, they might buy a soybean put option.
The fee you are paying to buy the call option is called the premium (it's essentially the cost of buying the contract which will allow you to eventually buy the stock or security). In this sense, the premium of the call option is sort of like a down-payment like you would place on a house or car. When purchasing a call option, you agree with the seller on a strike price and are given the option to buy the security at a predetermined price (which doesn't change until the contract expires).