Use the information below to answer questions 1 through 3. The Harrison originat
ID: 2798626 • Letter: U
Question
Use the information below to answer questions 1 through 3.
The Harrison originated a pool containing 40 ten-year fixed interest rate mortgages with an average balance of $50,000 each. All mortgages in the pool carry a coupon of 10%. (For simplicity, assume that all mortgage payments are made annually at 10% interest.). Assume a constant annual prepayment rate of 10% (for simplicity, assume that prepayments are based on the pool balance at the end of the preceding year and begin at the end of year 1). Below is the pool’s cash flows:
Principal
Principal and
End of
Pool
due to
Interest Pmts
Year
Balance
Prepayment
to Issuer
1
1,674,509
200,000
325,491
2
1,383,747
167,451
290,763
3
1,124,372
138,375
259,375
4
893,419
112,437
230,952
5
688,284
89,342
205,136
6
506,716
68,828
181,568
7
346,862
50,672
159,854
8
207,384
34,686
139,478
9
87,891
20,738
119,493
10
0
0
(A)
What is the initial mortgage pool balance?
$2,500,000
$2,000,000
$1,800,000
$3,000,000
Principal
Principal and
End of
Pool
due to
Interest Pmts
Year
Balance
Prepayment
to Issuer
1
1,674,509
200,000
325,491
2
1,383,747
167,451
290,763
3
1,124,372
138,375
259,375
4
893,419
112,437
230,952
5
688,284
89,342
205,136
6
506,716
68,828
181,568
7
346,862
50,672
159,854
8
207,384
34,686
139,478
9
87,891
20,738
119,493
10
0
0
(A)
Explanation / Answer
the initial pool balance is $2,000,000
reasons
1) since 40 mortgages obtained with an average of $50000 each,so total mortgage = 40*50000 = 2,000,000
2) since it is given ,prepayments are based on the pool balance at the end of the preceding year and begin at the end of year 1 ,
it means on the previous year ending balance, prepayments = previous year balance*10%
the payment will be started from 1 year onwards.
example = previous year balance 1674509 in 1st year ending
prepayment = 1674509*10% = 167451 (made in2nd year on previous year balance)
the series continue in the same manner for the followng year
example = 1383747*10% = 138374.7 ~138375 and so on
hence when prepayment is due in 1st year it must be 10% of beginning balance (because there was no previous year in this case. hence beginning balance taken)
i.e. lets initial pool balance be y
then , Y x 10% = 200,000
so , Y = 200,000/10% = 2,000,000
3) sumtotal of 1674509+325491 = 2,000,000
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