# Mortgage Repayment Calculator

## What is a Mortgage?

A mortgage is a type of loan, where the relationship between the lender and the borrower is tied around a real estate property. The loan is dedicated to buying and renovating a property, which offers some benefits for both sides. The lender has a relatively safe collateral for their money (as real estate can hardly be moved around or decrease in value quickly, under usual circumstances). The advantage for the borrower is, that since this kind of loan is a bit more secure than a loan not tied to real estate, the borrower offers a better interest rate than they would on different kinds of loans.

As far as mortgage payments go, this works very similarly to any other loan, where your monthly payments consist of paying off the principal, the interest, and, at times, some additional fees.

Monthly payments can change over time due to changing interest rates and the decreasing principal.

## Calculating Your Monthly Mortgage Repayment

Calculating the exact mortgage payment is a very difficult task, as it changes over time. Hence, the formula below is for approximative purposes only, as essentially, the monthly payment should be re-calculated each year or, in some cases, even each month, with the changing principal.

Our formula will be utilizing the following variables, in order to calculate the monthly payment (M).

Symbol | Description |
---|---|

r | The monthly interest rate of your mortgage in decimal form (simply take the percentage and divide it by 100 to achieve this form). The monthly rate is 1/12 the yearly rate. |

n | The number of total payments (this number can be easily calculated for monthly payments as the number of years you will be paying the mortgage off multiplied by 12). |

P | The principal amount, which is the value you have borrowed, which landed on your account. |

M=P*\cfrac{r(1+r)^n}{(1+r)^n-1}

This formula could be used to calculate the monthly payments based on your remaining principal on a yearly, or even monthly basis.

Most banks use a variety of other operations or constants in their formulae, in order to provide the users with a more balanced pay plan, as in the case of just using this formula, the payments would be quite high at the beginning of the loan and fairly low at the end, which is not preferred by most customers.

An attempt at averaging the costs is usually made, that is why it is best to ask the bank issuing the mortgage for a full payment breakdown.

We also have to keep in mind, that any additional fees or costs, like premature payment fees, late fees, etc. are not accounted for in this formula, as are some possible deductions.

### Worked-out Example

Gwen has a mortgage for her house. She currently has $40,000 left to pay on her principal, with a 5% interest rate. The mortgage is a 10-year mortgage. What will be her next monthly payment?

We have the following variables available:

**r**= 5% or 0.05 in decimal form for the yearly interest, hence 0.05÷12 = 0.0042 for monthly.**n**= 12×10 = 120 payments.**P**= 40,000.

Now we substitute the values into the formula and calculate the monthly payment. Keep in mind, that all values will be rounded to 4 decimal places as we calculate.

M=P*\cfrac{r(1+r)^n}{(1+r)^n-1}

=40,000*\cfrac{0.0042(1+0.0042)^{120}}{(1+0.05)^{120}-1}

=40,000*\cfrac{0.0069}{0.6536}

=40,000*0.0106=424

Hence, the first monthly fee will be $424.