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Circleville Mortgage Bank issues 10-year mortgages to private homebuyers. The bank issues $60 million worth of mortgages each year on average. While 25% of
Circleville Mortgage Bank issues 10-year mortgages to private homebuyers. The bank issues $60 million worth of mortgages each year on average. While 25% of mortgages persist for the full 10 years, 75% of mortgages are terminated early due to either prepayment or foreclosure. Assume that the 25%/75% breakdown applies to the dollar value of the mortgages as well as to the number of mortgages, i.e. assume that mortgages are effectively the same size. The bank reports that in steady state it holds a portfolio of mortgage obligations averaging $330 million. (Circleville does not buy or sell any mortgages through secondary markets.) (a) [2] Of the $330 million mortgage portfolio, what fraction represents mortgages that will persist for their full 10-year term? (b) [2] Among mortgages that are terminated before their 10-year term, how long do they persist on average before they are terminated?
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