Question

Consider the following pool of mortgages: 100 mortgages with initial balance of $166,669, interest rate 6.8%, issued for 30 years with monthly payments 50 mortgages with initial balance of $377,354, interest rate 3.8%, 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).

Answer 1

Weighted Average Maturity = [initial balance of mortgage 1/(initial balance of mortgage 1 + initial balance of mortgage 2)]*maturity of mortgage 1 in months + [initial balance of mortgage 2/(initial balance of mortgage 1 + initial balance of mortgage 2)]*maturity of mortgage 2 in months

for maturity of mortgages in months, maturity in years will be multiplied by 12 as there are 12 months in a year.

Weighted Average Maturity = [$166,669/($166,669 + $377,354)]*(30*12) + [$377,354/($166,669 + $377,354)]*(15*12)

Weighted Average Maturity = ($166,669/$544,023)*360 + ($377,354/$544,023)*180

Weighted Average Maturity = 0.3063638853504356*360 + 0.6936361146495644*180 = 110.2909987261568 + 124.8545006369216 = 235.15

the Weighted Average Maturity for this pool at origination is 235.15 months.