Derive mortgage formula using real numbers

[rbehl]

How can I develop mortgage repayment formula by working with some real numbers? If I take some real numbers say $500,000 of mortgage and then showing i pay say $3000 every month. I pay this amount every month towards mortgage repayment but it is just enough to take the value of my mortgage down a little bit and then i pay off interest and theres a pattern.

Here’s what I did:

i modelled it using geogebra and plotted graphs using 12 months of principal and interest data and that gave me 2 separate equations for principal and interest

Like y (subscript 1) = 2403.8022 * 0.9985 ^x
This equation shows interest

y(subscript 2) = 689.2027 * 1.005 ^x
This equation shows principal

on adding these 2, we get the monthly mortgage payment amount.

But it seems there’s still another way to derive the formula using numbers.

Can you share inputs what could be the other way to derive mortgage formula using real numbers?

 

[stapel]

How can I develop mortgage repayment formula by working with some real numbers? If I take some real numbers say $500,000 of mortgage and then showing i pay say $3000 every month. I pay this amount every month towards mortgage repayment but it is just enough to take the value of my mortgage down a little bit and then i pay off interest and theres a pattern.

Here’s what I did:

i modelled it using geogebra and plotted graphs using 12 months of principal and interest data and that gave me 2 separate equations for principal and interest

Like y (subscript 1) = 2403.8022 * 0.9985 ^x
This equation shows interest

y(subscript 2) = 689.2027 * 1.005 ^x
This equation shows principal

on adding these 2, we get the monthly mortgage payment amount.

But it seems there’s still another way to derive the formula using numbers.

Can you share inputs what could be the other way to derive mortgage formula using real numbers?

What is the interest rate on the loan?

Eliz.

Mortgage Professor: Formulas

 

[BigBeachBanana]

How can I develop mortgage repayment formula by working with some real numbers? If I take some real numbers say $500,000 of mortgage and then showing i pay say $3000 every month. I pay this amount every month towards mortgage repayment but it is just enough to take the value of my mortgage down a little bit and then i pay off interest and theres a pattern.

Here’s what I did:

i modelled it using geogebra and plotted graphs using 12 months of principal and interest data and that gave me 2 separate equations for principal and interest

Like y (subscript 1) = 2403.8022 * 0.9985 ^x
This equation shows interest

y(subscript 2) = 689.2027 * 1.005 ^x
This equation shows principal

on adding these 2, we get the monthly mortgage payment amount.

But it seems there’s still another way to derive the formula using numbers.

Can you share inputs what could be the other way to derive mortgage formula using real numbers?

1) What are you trying to model? The balance at time t?
2) How many payments are there?
3) What's the interest rate?
4) How did you come up with 3,000 monthly?
5) Are the payments made at the beginning of the month or the end of the month?

 

[JeffM]

The formula you are looking for requires the monthly payment, the amount being financed, the effective monthly interest rate, and the number of months before the loan is repaid. Given any three, you can find the fourth.

It is a rather ugly formula, but it is purely mechanical.