Question

1) A pool of mortgages contains 3.75%, 30-year loans with the total beginning balance of $99.57 million. In the first month, the total payments from the pool were $495.2 thousand. What are the total prepayments, to the nearest $0.01 thousand? E.g., if your answer is $25,345.39, record it as 25.35. Assume no defaults.

2) A pool of mortgages contains 3%, 15-year loans with the total beginning balance of $100 million. The pool backs 90 principal-only (PO) shares and 104 interest-only (IO) shares. Monthly expenses and fees amount to 0.04% of the beginning-of-the-month balance (they are subtracted from the interest portion). In the first month, the total payments from the pool were $699.7 thousand. What was the cash flow per PO share (to the nearest dollar)? Assume no defaults.

Answer 1

Capital Recovery factor (CRF) =(A/P, i,N)=(i*((1+i)^N))/(((1+i)^N)-1)

i=Interest Rate per period

N=number of periods

In this case,i=Monthly Interest=(3.75/12)%=0.3125%=0.003125

N= Number of months =30*12=360

CRF=(A/P,0.3125%,360)= (0.003125*(1.003125^360))/((1.003125^360)-1)=0.00463116

Monthly Payment =0.00463116*$99.57million=0.00463116*99570 (Thousand Million)=$461.12419 Thousand

Total Payments=$495.2 Thousands

Total Prepayment =(495.2-461.12419)=$34.075805 Thousands

Total Prepayment

34.08

(Nearest two decimals)

Monthly payment can also be calculated using excel PMT function with Rate=0.3125%, Nper=360 ,PV=-99570

Monthly Payment=PMT=461.12