# Mortgage Repayment

#### Definition:

This is type of mortgage in which monthly repayments include repayment of the capital along with the interest accrued. This is generally followed in UK.

The mortgage statement is generally received annually and this shows the amount borrowed decreases gradually throughout the life of the term.

Mortgage repayments are paid off over a predetermined period. During the initial years of repayment, most part of monthly payment goes into paying the interest accrued. The amount paid each year increases by the progress in the mortgage term.

Now-a-days many people are taking mortgage repayments over a period of 30 or 35 years so that they can keep their monthly repayments low in the initial years.

In this type of mortgage the term can be changed by contacting the lender and monthly repayment mortgages can be afforded to be increased. For this the mortgage lender charges some amount of fees.

Its advantage is that at the end of the term full amount of the debt is repaid.

It also erases the risk of investment which involves stock market performance.

The borrower does not suffer from negative equity because the mortgage balance will be reducing from month to month.

There is every likely chance that paying off the debt could be extended for another period.

#### Calculation:

Payment per period “pmt” is given by
Pmt =  pv * i/(1-(1+i) power –n) – fv * i/(1+i)power n -1
If the loan amortizes to 0 then
Pmt = pv * i/(1- (1+i)power –n)
In the above formula
Pv = present value of the value capital
I = interest rate per period
N = number of periods
Fv = future value of the capital after n periods

For example

A loan of \$10,000 over five years at the rate of 9% per annum the monthly payment is

\$10,000 * .0075/(1- (1+.0075) power -60) = \$207.58 per month.
In order to calculate the capital owing after a set of period the formula is
Fv = pv * (1+i)power of n
But when the case of regular payments the formula is
Fv = pv *(1+i) power of n- pmt ((( 1+i) power of n ) -1 )/i

For example:

For a mortgage of \$50,000 at the rate of 6% per annum compounded annually for a period of 25 years the capital owing after 5 years will be

First working on repayment
I= .06/12 = .005per month
Period n 25 *12 = 300 months
Therefore pmt = pv * (i/1- (1+i) power of -n)
So,
\$50,000 * (.005/(1-(1+.005)power of -300)) = \$322.15 per month
Calculating capital owing for 5 years i.e. for 60 months
\$50,000 *(1+.005) power of 60 - 322.15(((1+.005) power of 60)-1)/.005 = \$44,966