# Formula for calculating mortgage principal over time

November 10, 2011 6:20 PM Subscribe

Financial maths experts, mortgage brokers, bank employees: I need a formula for calculating expected mortgage principal owing at a given sale date, please. (Explanation inside.)

A person buys a property on date {Purchase Date} for an agreed price of {Purchase Price}, with a deposit of {Purchase Deposit}.

He/she takes out a mortgage for {Purchase Date Principal} for (approximately) the difference between {Purchase Price} and {Purchase Deposit}. These amounts are immediately paid to the vendor who then pays out his/her own mortgage, pays real estate agents and lawyers, etc.

The mortgage has an average annual interest rate of {Interest} over its lifespan, which is normally expressed as a percentage eg 7.75% and can be assumed to be compounded daily (365.24 days per annum). It is usually paid monthly at a minimum amount of {Repayment}, which should be calculable although I am unsure how exactly it is calculated. (Bonus question: how does that work?)

As time goes by the person presumably reduces the principal and thereby gains equity. Assuming they sold the house with a {Sale Date} of the next day for the same price they paid it, this would be approximately equal to {Deposit} (ignoring early termination and real estate agent fees).

However if {Sale Date} was ten years later and it sold for the same price, the equity would be the difference between the sale price and the principal of the mortgage at that time {Sale Date Principal}. If it were an interest-only loan, or set up in such a way (as I believe they commonly are) as to have reduction of the principal only start happening after a very long period of time, this could potentially end up being not much more than {Purchase Deposit} and if conditions were bad enough in that area, could be a lot less and even a negative figure (being under water on the mortgage).

I'd like a formula for estimating {Sale Date Principal}s, please. In practice the person may make more than minimum payments, redraw from equity, take out a second mortgage, etc - ignore these for this purpose. If they paid {Price} including a {Purchase Deposit} and a mortgage for the difference {Purchase Date Principal}, and just quietly paid each month and didn't mess around with their mortgage in any way, how much is {Sale Date Principal} as at {Sale Date}?

A person buys a property on date {Purchase Date} for an agreed price of {Purchase Price}, with a deposit of {Purchase Deposit}.

He/she takes out a mortgage for {Purchase Date Principal} for (approximately) the difference between {Purchase Price} and {Purchase Deposit}. These amounts are immediately paid to the vendor who then pays out his/her own mortgage, pays real estate agents and lawyers, etc.

The mortgage has an average annual interest rate of {Interest} over its lifespan, which is normally expressed as a percentage eg 7.75% and can be assumed to be compounded daily (365.24 days per annum). It is usually paid monthly at a minimum amount of {Repayment}, which should be calculable although I am unsure how exactly it is calculated. (Bonus question: how does that work?)

As time goes by the person presumably reduces the principal and thereby gains equity. Assuming they sold the house with a {Sale Date} of the next day for the same price they paid it, this would be approximately equal to {Deposit} (ignoring early termination and real estate agent fees).

However if {Sale Date} was ten years later and it sold for the same price, the equity would be the difference between the sale price and the principal of the mortgage at that time {Sale Date Principal}. If it were an interest-only loan, or set up in such a way (as I believe they commonly are) as to have reduction of the principal only start happening after a very long period of time, this could potentially end up being not much more than {Purchase Deposit} and if conditions were bad enough in that area, could be a lot less and even a negative figure (being under water on the mortgage).

I'd like a formula for estimating {Sale Date Principal}s, please. In practice the person may make more than minimum payments, redraw from equity, take out a second mortgage, etc - ignore these for this purpose. If they paid {Price} including a {Purchase Deposit} and a mortgage for the difference {Purchase Date Principal}, and just quietly paid each month and didn't mess around with their mortgage in any way, how much is {Sale Date Principal} as at {Sale Date}?

*It is usually paid monthly at a minimum amount of {Repayment}, which should be calculable although I am unsure how exactly it is calculated. (Bonus question: how does that work?)*

http://en.wikipedia.org/wiki/Mortgage_calculator#Monthly_payment_formula

posted by kithrater at 6:58 PM on November 10, 2011

Thanks folks. Amortization is the word that was missing from my vocabulary. :)

posted by aeschenkarnos at 7:45 PM on November 10, 2011

posted by aeschenkarnos at 7:45 PM on November 10, 2011

This thread is closed to new comments.

If you want to do the math yourself, the wikipedia page on loan amortization actually gives a rundown of what's required.

posted by jacquilynne at 6:46 PM on November 10, 2011