A Repayment Mortgage is the standard type of Mortgage used for home purchases. An amount of capital is borrowed with a property as security. The loan is repaid over over the term of the mortgage.
Periodic payments are made to cover the interest and re-pay some of the capital. Repayments are typically arranged to provide a consistent periodic payment - initially payments will mainly cover interest and only include a small amount of capital repayment - however over time, as the capital gradually reduces, the proportion of each payment that is required for interest will reduce.
A Variable Rate Mortgage (or Standard Variable Rate Mortgage) has an interest rate that may increase or decrease over time, however, the regular payments over the life of a standard repayment mortgage are calculated on the assumption that the underlying interest rate will remain the same. As the underlying interest rate changes, the regular payments needed to cover the interest and capital repayment will be adjusted.
Some companies offer Repayment Mortgages that vary the payments over time (a Low Start Mortgage) - for instance to provide a lower, more affordable, amount early in the mortgage - perhaps covering little more than the interest.
Some companies may offer Repayment Mortgages with "Mortgage Holidays" - a period when payments may be reduced (perhaps to cover the interest only) or deferred altogether.
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Remember, a mortgage is security for a loan in the form of the provision of a right in property, such as land or buildings. Typically, if terms of the loan are not met, then the lender has the right to sell the property to recover the debt.