Question

Consider a pool of 500 mortgages with the average size being $500 thousands, which is expected to be paid off in 30 years with fortnightly frequency (26 payments per year). The annual mortgage interest is 5%.

1. Estimate the value of fortnightly mortgage payments from the pool .
2. Suppose that the servicing fee is 0.6%, fill in the following table .

Fortnight	Begnning mortgage pool	Mortgage pool payment	Servicing fee	Net interest	Scheduled principal repayment	End of month balance
1
2
3
4
5
6
7
8
9
10

Answer 1

Service Fees would be the overhead the note holders (banks/investors) pay to the Mortgage agency to manage the mortgage administration. This is reduced from the payments made by the borrower and the net interest and principal amount is passed onto the originator.

In the above case, let us take the calculations for 1 Borrower having $500,000 loan and calculate the amounts. A simple multiplication of the values by 500 would give us the values for the pool.

Given that:

Loan period = 30 years = 30*12 = 360 months = 720 fortnightly payments

Annual Interest Rate = 5%. Therefore fortnightly interest rate = 5%/(12*2) = 0.21%

Loan Amount = $ 500,000

Service Fees = 0.6% divided by number of payments = 0.6%/720 = 0.0008% of the outstanding principal amount.

Therefore we can calculate the EMI using the formula

EMI Amount = Loan Amount * interest rate * (1+ interest rate)^(number of payments) / [(1+ interest rate)^(no. of payments) - 1]

This gives us the value of $ 1341.45 per fortnight

	Begin Mort. Pool	Mortgage Pool Payment	Servicing Fees	Net Interest	Principal Payment	End of Fortnight Balance	Loan Amount	500000
1	5,00,000.00	1,341.45	4.17	1,037.50	299.79	4,99,700.21	Number of Payments	720
2	4,99,700.21	1,341.45	4.16	1,036.88	300.41	4,99,399.80	Fortnight Interest	0.21%
3	4,99,399.80	1,341.45	4.16	1,036.25	301.04	4,99,098.77	Servicing Fees / EMI	0.0008%
4	4,99,098.77	1,341.45	4.16	1,035.63	301.66	4,98,797.10	Numerator	4661.14749
5	4,98,797.10	1,341.45	4.16	1,035.00	302.29	4,98,494.81	Denominator	3.47470159
6	4,98,494.81	1,341.45	4.15	1,034.38	302.92	4,98,191.89	EMI Amount	1341.4526
7	4,98,191.89	1,341.45	4.15	1,033.75	303.55	4,97,888.34
8	4,97,888.34	1,341.45	4.15	1,033.12	304.19	4,97,584.15
9	4,97,584.15	1,341.45	4.15	1,032.49	304.82	4,97,279.33
10	4,97,279.33	1,341.45	4.14	1,031.85	305.45	4,96,973.88

Therefore, the amount for the pool of 500 such mortgages would be:

	Begin Mort. Pool	Mortgage Pool Payment	Servicing Fees	Net Interest	Principal Payment	End of Fortnight Balance
1	25,00,00,000.00	6,70,726.30	2,083.33	5,18,750.00	1,49,892.97	24,98,50,107.03
2	24,98,50,107.03	6,70,726.30	2,082.08	5,18,438.97	1,50,205.24	24,96,99,901.79
3	24,96,99,901.79	6,70,726.30	2,080.83	5,18,127.30	1,50,518.17	24,95,49,383.62
4	24,95,49,383.62	6,70,726.30	2,079.58	5,17,814.97	1,50,831.75	24,93,98,551.86
5	24,93,98,551.86	6,70,726.30	2,078.32	5,17,502.00	1,51,145.98	24,92,47,405.88
6	24,92,47,405.88	6,70,726.30	2,077.06	5,17,188.37	1,51,460.87	24,90,95,945.01
7	24,90,95,945.01	6,70,726.30	2,075.80	5,16,874.09	1,51,776.42	24,89,44,168.59
8	24,89,44,168.59	6,70,726.30	2,074.53	5,16,559.15	1,52,092.62	24,87,92,075.98
9	24,87,92,075.98	6,70,726.30	2,073.27	5,16,243.56	1,52,409.48	24,86,39,666.50
10	24,86,39,666.50	6,70,726.30	2,072.00	5,15,927.31	1,52,727.00	24,84,86,939.50