Consider the following pool of mortgages: 100 mortgages with initial balance of $327,344, interest rate 2.1%, issued for 30 years with monthly payments 50 mortgages with initial balance of $366,012, interest rate 4%, issued for 15 years with monthly payments What is the Weighted Average Maturity for this pool at origination? Express your answer in months rounded to 2 decimal points (e.g. if your answer is 5.6744 months, write 5.67).
Weighted Average Maturity = (weight of mortgage 1*maturity of mortgage 1) + (weight of mortgage 2*maturity of mortgage 2)
weight of mortgage 1 = initial balance of mortgage 1/(initial balance of mortgage 1 + initial balance of mortgage 2)
weight of mortgage 1 = $327,344/($327,344 + $366,012) = $327,344/$693,356 = 0.47
weight of mortgage 2 = initial balance of mortgage 2/(initial balance of mortgage 1 + initial balance of mortgage 2)
weight of mortgage 1 = $366,012/($327,344 + $366,012) = $366,012/$693,356 = 0.53
Weighted Average Maturity = (0.47*30 years) + (0.53*15) = 14.1 years + 7.95 years = 22.05 years or 22.05*12 = 264.60 months
the Weighted Average Maturity for this pool at origination is 264.60 months.
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