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What are mortgages

what are mortgages

Mortgage loan types

There are many types of mortgage loans. The two basic types of amortized loans are the fixed rate mortgage (FRM) and adjustable rate mortgage (ARM).

In a FRM, the interest rate, and hence monthly payment, remains fixed for the life (or term) of the loan. In the US, the term is usually for 10, 15, 20, or 30 years. In the UK the fixed term can be as short as five years, after which the loan reverts to a variable rate (which makes the loan an ARM).

In an ARM, the interest rate is fixed for a period of time, after which it will periodically (annually or monthly) adjust up or down to some market index. Common indices in the US include the Prime Rate, the LIBOR, and the Treasury Index ("T-Bill"). Other indexes like COFI, COSI, and MTA, are also available but are less popular.

Adjustable rates transfer part of the interest rate risk from the lender to the borrower, and thus are widely used where unpredictable interest rates make fixed rate loans difficult to obtain. Since the risk is transferred, lenders will usually make the initial interest rate of the ARM's note anywhere from 0.5% to 2% lower than the average 30-year fixed rate.

In most scenarios, the savings from an ARM outweigh its risks, making them an attractive option for people who are planning to keep a mortgage for ten years or less.

A partial amortization or balloon loan is one where the amount of monthly payments due are calculated (amortized) over a certain term, but the outstanding principal balance is due at some point short of that term. A balloon loan can be either a Fixed or Adjustable in terms of the Interest Rate. Many Second Trust mortgages use this feature. The most common way of describing a balloon loan uses the terminology X due in Y, where X is the number of years over which the loan is amortized, and Y is the year in which the principal balance is due.

Other loan types:

Costs involved in a mortgage

Lenders may charge various fees when giving a mortgage to a mortgagee. These include entry fees, exit fees, administration fees and lenders mortgage insurance.

Fixed rate mortgage calculations

First the nomenclature.

I - The stated interest rate, for example, 5%/year. This is not the APR (annualized percentage rate).

m - The number of periods in the time frame of I. I is usually based on a year but it could be based on any amount of time.

i - The interest rate for the compounding period which is needed for the calculation. For example, a real property mortgage is usually based on a monthly period. In this case i=I*1/12 where I is based on the normal yearly period. In general i=I/m. Also I needs to be a decimal not a percent thus it also needs to be divided by 100.

n - The total number of periods or payments. Things like mortgages usually cover multiple years.

B - The balance, for example, the balance remaining on the mortgage at any point in time.

Mortgage Calculations:

Let B0 be the original mortgage.

Let B1. B2. B3 etc. be the balance after the first, second, third period respectively.

Obviously, one can think of B0 as the balance after the zeroth period namely the beginning balance.

P - The mortgage payment.

Now lets write down the balances. First the initial balance, the amount of the mortgage.

Now calculate the balance after one period or payment.

During the first period the initial balance has grown by the period interest and has been decreased by the first payment. Similarly


After n periods or payments we have

Bn is set equal to zero. When the mortgage is paid off the balance is zero. Now one can solve for P the payment. Rearranging gives:

The righthand side is a geometric series where each term is equal to the preceding term multiplied by (1 + i) which is known as the common ratio. See geometric sequence for additional details.

Solving for P gives:

The payment can be readily calculated to the penny with a spread sheet or scientific calculator.

Note: B0 is just a simple multiplier. Therefore one can do the calculation for a unit of currency such as a dollar and then multiply the result by the amount of the loan. In essence B0 is just a scale factor. For example think of the loan amount as my dollar where my dollar is just a currency whose exchange rate is just the loan amount difference.

Now lets do some calculations. Mortgages are usually for 10, 15, 20 or 30 years. Interest rates used to be around 9%/year and today around 6%/year. For all calculations B0 = 1

years, n, (1 + i)^n, P, nP for i = .09/12 = .0075

years, n, (1 + i)^n, P, nP for i = .06/12 = .005

First calculate (1 + i)^n since it occurs in both the numerator and the denominator. Then complete the calculation for the payment P. In the first case, for each dollar of loan the payment is a little over a penny per month. Multiplying the amount of the payment P by the number of payments n gives the total amount paid. In the first case, for each dollar of loan the repayment is a little over a dollar and 82 cents. The 1.82 is also the ratio of the repayment amount to the amount of the loan.

Islamic mortgages

Islamic Sharia law prohibits the payment or receipt of interest. which means that practising Muslims cannot use conventional mortgages. However, real estate is far too expensive for most people to buy outright using cash: Islamic mortgages solve this problem by having the property change hands twice. In one variation, the bank will buy the house outright and then act as a landlord. The homebuyer, in addition to paying rent. will pay a contribution towards the purchase of the property. When the last payment is made, the property changes hands.

An alternative scheme involves the bank reselling the property according to an installment plan, at a price higher than the original price.

In the United Kingdom. HSBC was the first major bank to offer Islamic mortgages.

Torrens title registration system

Under the Torrens title registration system of land ownership registration, mortgages and easements are recorded on the title at the central registry, so that any buyer knows for certain whether a block of land is subject to a mortgage or not. This is a simple process, which reduces transaction costs involved in the sale of land.

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