Which term describes a mortgage with varying interest rates over its term?

The term that describes a mortgage with varying interest rates over its term is the Adjustable Rate Mortgage (ARM). This type of mortgage features an interest rate that may change periodically. These changes are typically based on a specific benchmark or index that reflects the cost of borrowing. While the initial rate of an ARM can often be lower than that of a fixed-rate mortgage, it can fluctuate at intervals defined in the loan agreement, meaning that the borrower's monthly payments can increase or decrease over time.

In contrast, a fully amortized mortgage involves fixed payments over the life of the loan with a consistent interest rate, which does not change. A fixed-rate mortgage maintains the same interest rate throughout the term, providing stability in payment amounts. A balloon mortgage generally has lower monthly payments with a larger lump-sum payment due at the term's end, but it does not have a varying interest rate structure like an ARM. Thus, the key feature of an ARM is its ability to adapt to changing market conditions through variable interest rates, making it the correct answer.