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A fixed rate mortgage is a type of mortgage where the interest rate is fixed for the entire term of the loan. The interest rate is usually a bit higher than other types of mortgages but there's no way the interest rate can increase in the future.
An adjustable rate mortgage is a type of mortgage where the interest rate is fixed for an initial period of time. At the end of that period, the interest rate is allowed to change by the adjustment amount each adjustment period. The interest rate continues to change until the term is up or until it hits the interest rate cap.
A balloon mortgage is a type of mortgage where the interest rate is fixed for an initial period of time. At the end of that period, the remaining balance is due in full. At that point, unless the homeowner can pay off the remaining balance, he/she must seek out another mortgage. For example, a 5/25 balloon mortgage has an fixed initial period of 5 years at which point the interest rate changes depending on the market for the next 25 years.