Home equity price

Home equity is the value of the home minus what you owe on your mortgages.

In your case equity is

Equity =   Value    - Mortgage
Equity =   $200,000 - $50,000
Equity =   $150,000

Now if you are trying to tap into that equity by getting a 2nd mortgage or home equity loan keep in mind that the bank won't allow you to tap into all that equity. Also selling the house comes with costs, so you won't have $150,000 in cash if you were to sell the house today.

Think of it this way. When you bought the house originally for $100,000, let's say you put in $10,000 of yours and got a loan of $90,000 from the bank. So you began with $10,000 of your own money i.e. equity i.e the cushion against market for the bank.

'Equity' is the residual interest after the charges are paid off. Now, when you finance your purchase using a loan, you enter a contract to pay a stream of cashflows to the bank and yes, some interest. While the asset is in your name, there is still a fixed charge of $50,000, without discharging the said charge, you wouldn't have a clear title.

So, in layman's terms, your equity is the $ you are left with after you discharge your obligation to the bank. In your case, if your valuation is correct, that would be $200,000 - $50,000 - prepayment penalty = $150,000 - prepayment penalty.

Equity = Value - Debt

So, equity is $150k in your example.

Appreciation = Value - Purchase Price

Appreciation is $100k in your example.

Capital Gain (when you sell) = Sales price - purchase price - depreciation.