An adjustable rate mortgage allows the rate of interest to fluctuate over the te
ID: 3020691 • Letter: A
Question
An adjustable rate mortgage allows the rate of interest to fluctuate over the term of the loan, depending on economic conditions. A fixed rate mortgage holds the rate of interest constant. Which sequence of monthly payments has smaller variance, those on an adjustable rate mortgage or those on a fixed rate mortgage? Choose the correct answer below.
A. Since the variance for the fixed rate mortgage is greater than zero and the variance for the adjustable rate mortgage is equal to zero if the rate of interest increases and less than zero if the rate of interest decreases, the sequence of monthly payments with smaller variance depends on economic conditions.
B. Since the variance for the fixed rate mortgage is greater than zero and the variance for the adjustable rate mortgage is equal to zero, the sequence of monthly payments for the adjustable rate mortgage has smaller variance.
C. Since the variance for the fixed rate mortgage is equal to zero and the variance for the adjustable rate mortgage is greater than or equal to zero, the sequence of monthly payments for the fixed rate mortgage has smaller variance.
D. Since the variance for the fixed rate mortgage is equal to zero and the variance for the adjustable rate mortgage is greater than zero if the rate of interest increases and less than zero if the rate of interest decreases, the sequence of monthly payments with smaller variance depends on economic conditions.
Explanation / Answer
In fixed rate mortgage monthly payments remain constant so fixed rate mortgage has variance zero.
Variance cannot be negative so the variance for the adjustable rate mortgage is greater than or equal to zero, the sequence of monthly payments for the fixed rate mortgage has smaller variance.
Option option C is correct.
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