The 3/1 residential adjustable rate mortgage (ARM) is a specic type of adjustable-rate

mortgage that has an initial interest rate for the rst three years, and thereafter adjusts

each year. These loans are typically amortized over 30 years.

Suppose that every year the average number of 3/1 ARM loans issued in the US is

8 million. Assume that the number of borrowers pre-paying, delinquent or going into

foreclosure during the initial three year period of their loan is negligible. Subsequently,

once the initial three-year period is over, 70% of loans will eventually be pre-paid, i.e.,

paid-o before they are fully amortized (most of these because of re-nancing), 9% of

loans will eventually become delinquent or enter into foreclosure, and the remaining 21%

will be held until maturity and paid-o in full at that time.

(a) [2] At any given time, what is the average number of 3/1 ARM loans in their initial

three year period?

(b) [2] It is estimated that at any given time, the total number of 3/1 ARM loans that

are delinquent or in foreclosure is 5,220,000 (all of which are past their initial three

year period). On average, how long did it take for these loans to become delinquent

or in foreclosure (in years) from the moment their initial 3 year period was

over?