Mortgage Payments- How Much Comes Off The Loan?
How To Calculate The Capital And Interest Components Of Mortgages
Oct 16, 2009
Mortgage and loan repayments are made up of two main parts, the capital and the interest. The capital is the amount borrowed at the start of the loan period, and the interest is a charge for borrowing the money. At the start of a loan, most of the repayment is used to cover interest costs. As more payments are made, the amount of interest paid falls, and the amount of capital paid back increases.
What Is The Mortgage Interest Rate?
Before doing any calculations the interest rate needs to be defined exactly, because the payment period is key to figuring out what the interest rate really is. An interest rate of 1% per month is not the same as 12% per year. This may seem odd, but there is a difference. An interest rate of 1% per month is equivalent to about 12.7% per year. The difference is due to compound interest- interest paid on the interest. In the Financial Functions used by Microsoft Excel, the difference is taken care of, so this may be used to do the calculations. The formula to calculate monthly interest from the annual interest rate of 12% is:
(1+12 / 100)^(1/12) - 1, and for monthly to annual interest rate, for 1% per month is:
(1+1/100)^12 - 1
How Are Mortgage Repayments Calculated?
The total mortgage payment - capital plus interest, is easily obtained using the Excel PMT formula. This is described in detail in the article Get an Instant Mortgage Calculator Free. Using these values:
Interest Rate = 6% per annum
Number of payments = 300 (25 years times 12 payments per year)
Mortgage Amount = $100,000
Amount of Loan Outstanding at End = 0
The payment each month is
=PMT(0.06/12,300,100000,0,0)
= -$644.30 (The figure is shown as a negative number.)
The total amount repaid for the $100,000 mortgage is
$644.30 x 300 = $193,290
Mortgage Payments Reduce The Mortgage Amount By How Much?
This varies with the outstanding mortgage balance just before the payment is made. The very last mortgage payment is almost all capital, with very little interest. The very first payment is mostly interest repayment. For a mortgage of $100,000 the payments were calculated as $644.30 per month. The interest portion of this can be calculated from the formula shown. First, the monthly interest rate needs to be worked out:
= (1 + 0.06)^(1/12)
= 0.00486755 (about 0.49% per month).
So the interest charge is
Outstanding Amount x Interest Rate
= $100000 x 0.0048676
=$486.76
So the monthly payment of $644.30 is used to pay $486.76 interest, and the other $157.54 pays off the principal, or loan borrowed. This leaves a balance of
$100,000 - $157.54 = $99,842.46
After the second monthly payment of $644.30, the amount paid in interest is
$99,842.46 x 0.0048676 = $485.99
Mortgage Repayment and Balance By Month
Microsoft Excel is ideal for setting up a repayments and balance schedule. Figure 1 shows how to do this.
- The amount borrowed is entered into cell A2.
- The monthly interest rate is entered into each of the cells in column B.
- The Interest Paid is calculated in cell C2, as A2 x B2.
- The capital paid is the monthly payment - C2.
- The new balance is A2 - D2.
- In the next row, the Outstanding Balance is the New Balance from the previous row.
- All that is then needed is to copy the cell formula down each column, as far as necessary.
Mortgage Repayment Summary and Caveat
Many people are curious as to why it takes so long to pay off a mortgage. This has been demonstrated, as well as how to calculate capital and interest payments for each month. Further details about how to calculate the loan reduction are available at "Mortgage Repayments - Capital Repaid By Year". The term of a mortgage may be reduced by making overpayments, especially early in the term.
This article is intended to explain general principles and give guidance as to how mortgage payments are used. It is not a substitute for professional advice. Many mortgage providers offer free online mortgage calculators.
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