# frm

Document Sample

```					                    LESSON #4: REVIEW OF
FIXED RATE MORTGAGES

The fixed rate mortgage has long been the favorite form of residential
real estate financing in the United States. Although alternative
financing techniques have gained in popularity in the past two decaeds,
the fixed rate mortgage is still the basis for most real estate
financing.

The concepts behind a fixed rate mortgage are relativly simple. An
initial loan is made from the lender to the borrower, and then the
borrower makes a series of even cash flows for a fixed length of time
that will repay the loan. The interest rate on the loan stays the same
for the life of the loan. Some of each payment is used to pay interest
while the rest is used to repay principal. Note that this is different
from an instrument such as a treasury bond in which all of the principal
is repaid at the termination of the bond.

The amounts that go toward the repayment of principal and interest
change with each payment (although the total amount of each payment
remains the same.) The reason for this is fairly straightforward. The
amount of interest that is due at any payment date can be calculated by
multiplying the periodic interest rate by the current outstanding
balance on the loan. Since some principal is repaid with each payment,
the principal balance outstanding in a given period is less than the
principal balance that was outstanding in the previous period. Since the
total payment made each month is constant, and the interest owed
decreases with each payment, the amount of principal that is repaid in
each period increases with each payment.

In the early years of a mortgage, most of the payment goes toward
paying interest, while in the latter years most of the payment goes to
the repayment of principal. Knowing the amount out of each payment that
goes to interest and to principal can be quite important. Under our
current tax system, 100% of the interest payments on home mortgages
(excluding rental property) can be deducted from taxable income. Thus
a large portion of income can be shielded from taxed by using a mortgage
to finance a house. One can break down the amount of each payment of a
mortgage that goes toward principal and interest. This is called
amortizing the mortgage. The results are put into an amortization table.
In general this table will contain six peices of information, the
time of each payment, the amount of each payment, the amount of each
payment that goes toward principal repayment, the amount that goes to
interest payment, the outstanding principal balance after each payment,
and the proportion outstanding. The proportion outstanding is simply the
percentage of the original loan balance to the current balance. For
example, if a mortgage with an original balance of \$1,000,000 had a
current outstanding balance of \$875,000, the proportion outstanding
would be
\$ 875,000
---------- = .875 = 87.5%
\$1,000,000

An example of an amortization table is provided in the work area of this

One important idea about the amortization schedule. This schedule is
only valid if payments are made on time. The borrower usually has the
right to pay off any or all of the loan at any time. If the borrower
does prepay, obviously the amortization schedule will no longer be
accurate. Similarly if a payment is late interest will accrue to an
amount that is greater than the amount shown on the amortization
schedule.

It is fairly obvious that one of the major hurdles with fixed rate
mortgages is finding a payment that will exactly pay off the loan at the
end of the loan period. Note that this is essentially an annuity
problem similar to the ones studied in lesson #2. Here we know the
present value of the annuity, the interest rate, and the length of time
of the annuity, the only information we do not have is the actual
annuity payment amount. Recall that the present value of an annuity
is given by:
n
1-[1/(1+i) ]
PVA = ANN ------------
i,n                i

Where
n = number of periods until loan is fully paid.
i = periodic interest rate of loan.
ANN = amount of annuity payments.
PVA = present value of annuity at interest rate i and n
i,n months to maturity.

Rearranging terms, we get

i
ANN     = PVA * -------------
i,n                       n
1-[1/(1+i) ]

We now have a direct way of calculating the payment neccesary to
amortize a loan in n periods with periodic interest rate i. The formula

i
------------ = M.C.
n
1-[1/(1+i) ]

is called the mortgage constant (M.C.) Again note that n is the number
of periods and i is the periodic interest rate. If one is calculating
a mortgage constant for a typical mortgage, the payments are monthly but
the interest rate and length of the mortgage are usually quoted in
annual (yearly) terms. One must then divide the interest rates by 12
and multiply the number of periods by 12 also. Be sure to convert
all rates and lengths of time into the correct units.

End of Review Section……Go to Next Sheet
FIXED RATE MORTGAGE: WORK AREA

On the following page you will find an area for examining the basics
of a fixed rate mortgage. You will input the total amount of principal,
the interest rate on the mortgage, and the remaining mortgage term in
months.

Note that the principal remaining column shows the amount of principal
that is owed before the payment for that month is paid.

You may also calculate the effective yield on a mortgage which has
features such as points and prepayment penalties, or which prepays
prior to maturity. In addition you may solve for a price of a mortgage
in the secondary market if a market discount rate is supplied.

INPUT:                      30 Year Fixed Rate Monthly Payment Mortgage

Initial Principal                   \$100,000
Contract Rate                        10.00%
Months until Prepayment                   360
Points                                      2   % of initial principal
Prepayment Penalty                     2.00%    of outstanding prin. balance
Market Discount Rate               10.0000%     ONLY use to calc. market price
Servicing Rate                         0.00%    of outstanding balance (yrly)

OUTPUT:

Monthly Payment                      \$877.57
Mortgage Constant                    0.00878
Total Interest Paid              \$215,925.77
Servicing Contract Value                \$0.00
Market Price                     \$100,000.00
Effective Yield                    10.2417%

***Scroll right to see the mortgage pricing model***

End of Work Section
PRICING MODEL

Principal   Portion
Month    Remaining    Outstand.
0     \$100,000.00
1     \$100,000.00   100.00%
2      \$99,955.76    99.96%
3      \$99,911.15    99.91%
4      \$99,866.18    99.87%
5      \$99,820.82    99.82%
6      \$99,775.09    99.78%
7      \$99,728.98    99.73%
8      \$99,682.48    99.68%
9      \$99,635.60    99.64%
10      \$99,588.32    99.59%
11      \$99,540.65    99.54%
12      \$99,492.59    99.49%
13      \$99,444.12    99.44%
14      \$99,395.25    99.40%
15      \$99,345.97    99.35%
16      \$99,296.28    99.30%
17      \$99,246.18    99.25%
18      \$99,195.66    99.20%
19      \$99,144.72    99.14%
20      \$99,093.36    99.09%
21      \$99,041.56    99.04%
22      \$98,989.34    98.99%
23      \$98,936.68    98.94%
24      \$98,883.58    98.88%
25      \$98,830.04    98.83%
26      \$98,776.05    98.78%
27      \$98,721.61    98.72%
28      \$98,666.72    98.67%
29      \$98,611.37    98.61%
30      \$98,555.56    98.56%
31      \$98,499.28    98.50%
32      \$98,442.54    98.44%
33      \$98,385.32    98.39%
34      \$98,327.63    98.33%
35      \$98,269.45    98.27%
36      \$98,210.79    98.21%
37   \$98,151.65   98.15%
38   \$98,092.00   98.09%
39   \$98,031.87   98.03%
40   \$97,971.23   97.97%
41   \$97,910.08   97.91%
42   \$97,848.43   97.85%
43   \$97,786.26   97.79%
44   \$97,723.57   97.72%
45   \$97,660.37   97.66%
46   \$97,596.63   97.60%
47   \$97,532.36   97.53%
48   \$97,467.56   97.47%
49   \$97,402.22   97.40%
50   \$97,336.33   97.34%
51   \$97,269.90   97.27%
52   \$97,202.91   97.20%
53   \$97,135.36   97.14%
54   \$97,067.25   97.07%
55   \$96,998.57   97.00%
56   \$96,929.32   96.93%
57   \$96,859.50   96.86%
58   \$96,789.09   96.79%
59   \$96,718.09   96.72%
60   \$96,646.50   96.65%
61   \$96,574.32   96.57%
62   \$96,501.53   96.50%
63   \$96,428.14   96.43%
64   \$96,354.14   96.35%
65   \$96,279.52   96.28%
66   \$96,204.28   96.20%
67   \$96,128.41   96.13%
68   \$96,051.91   96.05%
69   \$95,974.77   95.97%
70   \$95,896.98   95.90%
71   \$95,818.55   95.82%
72   \$95,739.47   95.74%
73   \$95,659.73   95.66%
74   \$95,579.32   95.58%
75   \$95,498.24   95.50%
76   \$95,416.49   95.42%
77   \$95,334.06   95.33%
78   \$95,250.94   95.25%
79   \$95,167.12   95.17%
80   \$95,082.61   95.08%
81   \$94,997.39   95.00%
82   \$94,911.47   94.91%
83   \$94,824.82   94.82%
84   \$94,737.46   94.74%
85   \$94,649.37   94.65%
86   \$94,560.54   94.56%
87   \$94,470.97   94.47%
88   \$94,380.66   94.38%
89   \$94,289.59   94.29%
90   \$94,197.77   94.20%
91   \$94,105.18   94.11%
92   \$94,011.82   94.01%
93   \$93,917.68   93.92%
94   \$93,822.75   93.82%
95   \$93,727.04   93.73%
96   \$93,630.52   93.63%
97   \$93,533.21   93.53%
98   \$93,435.08   93.44%
99   \$93,336.13   93.34%
100   \$93,236.36   93.24%
101   \$93,135.76   93.14%
102   \$93,034.32   93.03%
103   \$92,932.03   92.93%
104   \$92,828.90   92.83%
105   \$92,724.90   92.72%
106   \$92,620.04   92.62%
107   \$92,514.30   92.51%
108   \$92,407.68   92.41%
109   \$92,300.17   92.30%
110   \$92,191.77   92.19%
111   \$92,082.46   92.08%
112   \$91,972.24   91.97%
113   \$91,861.11   91.86%
114   \$91,749.04   91.75%
115   \$91,636.05   91.64%
116   \$91,522.11   91.52%
117   \$91,407.22   91.41%
118   \$91,291.38   91.29%
119   \$91,174.57   91.17%
120   \$91,056.78   91.06%
121   \$90,938.02   90.94%
122   \$90,818.26   90.82%
123   \$90,697.51   90.70%
124   \$90,575.75   90.58%
125   \$90,452.98   90.45%
126   \$90,329.18   90.33%
127   \$90,204.35   90.20%
128   \$90,078.49   90.08%
129   \$89,951.57   89.95%
130   \$89,823.59   89.82%
131   \$89,694.55   89.69%
132   \$89,564.43   89.56%
133   \$89,433.23   89.43%
134   \$89,300.94   89.30%
135   \$89,167.54   89.17%
136   \$89,033.03   89.03%
137   \$88,897.40   88.90%
138   \$88,760.64   88.76%
139   \$88,622.74   88.62%
140   \$88,483.69   88.48%
141   \$88,343.49   88.34%
142   \$88,202.11   88.20%
143   \$88,059.56   88.06%
144   \$87,915.82   87.92%
145   \$87,770.88   87.77%
146   \$87,624.73   87.62%
147   \$87,477.36   87.48%
148   \$87,328.77   87.33%
149   \$87,178.94   87.18%
150   \$87,027.86   87.03%
151   \$86,875.52   86.88%
152   \$86,721.91   86.72%
153   \$86,567.02   86.57%
154   \$86,410.84   86.41%
155   \$86,253.36   86.25%
156   \$86,094.56   86.09%
157   \$85,934.45   85.93%
158   \$85,773.00   85.77%
159   \$85,610.20   85.61%
160   \$85,446.05   85.45%
161   \$85,280.53   85.28%
162   \$85,113.63   85.11%
163   \$84,945.33   84.95%
164   \$84,775.64   84.78%
165   \$84,604.53   84.60%
166   \$84,432.00   84.43%
167   \$84,258.03   84.26%
168   \$84,082.61   84.08%
169   \$83,905.72   83.91%
170   \$83,727.37   83.73%
171   \$83,547.52   83.55%
172   \$83,366.18   83.37%
173   \$83,183.33   83.18%
174   \$82,998.95   83.00%
175   \$82,813.04   82.81%
176   \$82,625.57   82.63%
177   \$82,436.55   82.44%
178   \$82,245.95   82.25%
179   \$82,053.76   82.05%
180   \$81,859.97   81.86%
181   \$81,664.56   81.66%
182   \$81,467.53   81.47%
183   \$81,268.85   81.27%
184   \$81,068.52   81.07%
185   \$80,866.52   80.87%
186   \$80,662.84   80.66%
187   \$80,457.46   80.46%
188   \$80,250.36   80.25%
189   \$80,041.55   80.04%
190   \$79,830.99   79.83%
191   \$79,618.67   79.62%
192   \$79,404.59   79.40%
193   \$79,188.72   79.19%
194   \$78,971.06   78.97%
195   \$78,751.58   78.75%
196   \$78,530.27   78.53%
197   \$78,307.12   78.31%
198   \$78,082.11   78.08%
199   \$77,855.22   77.86%
200   \$77,626.44   77.63%
201   \$77,395.76   77.40%
202   \$77,163.15   77.16%
203   \$76,928.60   76.93%
204   \$76,692.10   76.69%
205   \$76,453.63   76.45%
206   \$76,213.18   76.21%
207   \$75,970.71   75.97%
208   \$75,726.23   75.73%
209   \$75,479.71   75.48%
210   \$75,231.14   75.23%
211   \$74,980.49   74.98%
212   \$74,727.76   74.73%
213   \$74,472.92   74.47%
214   \$74,215.95   74.22%
215   \$73,956.85   73.96%
216   \$73,695.58   73.70%
217   \$73,432.14   73.43%
218   \$73,166.51   73.17%
219   \$72,898.65   72.90%
220   \$72,628.57   72.63%
221   \$72,356.24   72.36%
222   \$72,081.64   72.08%
223   \$71,804.74   71.80%
224   \$71,525.55   71.53%
225   \$71,244.02   71.24%
226   \$70,960.15   70.96%
227   \$70,673.91   70.67%
228   \$70,385.29   70.39%
229   \$70,094.26   70.09%
230   \$69,800.81   69.80%
231   \$69,504.91   69.50%
232   \$69,206.55   69.21%
233   \$68,905.70   68.91%
234   \$68,602.34   68.60%
235   \$68,296.45   68.30%
236   \$67,988.02   67.99%
237   \$67,677.01   67.68%
238   \$67,363.42   67.36%
239   \$67,047.21   67.05%
240   \$66,728.36   66.73%
241   \$66,406.86   66.41%
242   \$66,082.68   66.08%
243   \$65,755.80   65.76%
244   \$65,426.19   65.43%
245   \$65,093.84   65.09%
246   \$64,758.72   64.76%
247   \$64,420.80   64.42%
248   \$64,080.07   64.08%
249   \$63,736.50   63.74%
250   \$63,390.06   63.39%
251   \$63,040.74   63.04%
252   \$62,688.51   62.69%
253   \$62,333.34   62.33%
254   \$61,975.22   61.98%
255   \$61,614.10   61.61%
256   \$61,249.98   61.25%
257   \$60,882.83   60.88%
258   \$60,512.61   60.51%
259   \$60,139.31   60.14%
260   \$59,762.90   59.76%
261   \$59,383.36   59.38%
262   \$59,000.65   59.00%
263   \$58,614.75   58.61%
264   \$58,225.63   58.23%
265   \$57,833.27   57.83%
266   \$57,437.65   57.44%
267   \$57,038.72   57.04%
268   \$56,636.47   56.64%
269   \$56,230.87   56.23%
270   \$55,821.89   55.82%
271   \$55,409.50   55.41%
272   \$54,993.67   54.99%
273   \$54,574.38   54.57%
274   \$54,151.60   54.15%
275   \$53,725.29   53.73%
276   \$53,295.43   53.30%
277   \$52,861.99   52.86%
278   \$52,424.93   52.42%
279   \$51,984.23   51.98%
280   \$51,539.86   51.54%
281   \$51,091.79   51.09%
282   \$50,639.99   50.64%
283   \$50,184.41   50.18%
284   \$49,725.05   49.73%
285   \$49,261.85   49.26%
286   \$48,794.79   48.79%
287   \$48,323.85   48.32%
288   \$47,848.97   47.85%
289   \$47,370.14   47.37%
290   \$46,887.32   46.89%
291   \$46,400.48   46.40%
292   \$45,909.58   45.91%
293   \$45,414.59   45.41%
294   \$44,915.47   44.92%
295   \$44,412.19   44.41%
296   \$43,904.72   43.90%
297   \$43,393.02   43.39%
298   \$42,877.06   42.88%
299   \$42,356.80   42.36%
300   \$41,832.20   41.83%
301   \$41,303.23   41.30%
302   \$40,769.85   40.77%
303   \$40,232.03   40.23%
304   \$39,689.72   39.69%
305   \$39,142.90   39.14%
306   \$38,591.52   38.59%
307   \$38,035.54   38.04%
308   \$37,474.94   37.47%
309   \$36,909.66   36.91%
310   \$36,339.66   36.34%
311   \$35,764.92   35.76%
312   \$35,185.39   35.19%
313   \$34,601.03   34.60%
314   \$34,011.80   34.01%
315   \$33,417.66   33.42%
316   \$32,818.57   32.82%
317   \$32,214.49   32.21%
318   \$31,605.37   31.61%
319   \$30,991.18   30.99%
320   \$30,371.87   30.37%
321   \$29,747.39   29.75%
322   \$29,117.72   29.12%
323   \$28,482.79   28.48%
324   \$27,842.58   27.84%
325   \$27,197.03   27.20%
326   \$26,546.10   26.55%
327   \$25,889.74   25.89%
328   \$25,227.92   25.23%
329   \$24,560.58   24.56%
330   \$23,887.68   23.89%
331   \$23,209.17   23.21%
332   \$22,525.01   22.53%
333   \$21,835.15   21.84%
334   \$21,139.54   21.14%
335   \$20,438.13   20.44%
336   \$19,730.87   19.73%
337   \$19,017.73   19.02%
338   \$18,298.64   18.30%
339   \$17,573.55   17.57%
340   \$16,842.43   16.84%
341   \$16,105.21   16.11%
342   \$15,361.85   15.36%
343   \$14,612.29   14.61%
344   \$13,856.49   13.86%
345   \$13,094.39   13.09%
346   \$12,325.94   12.33%
347   \$11,551.08   11.55%
348   \$10,769.77   10.77%
349    \$9,981.95    9.98%
350    \$9,187.56    9.19%
351    \$8,386.55    8.39%
352    \$7,578.86    7.58%
353    \$6,764.45    6.76%
354    \$5,943.25    5.94%
355    \$5,115.20    5.12%
356    \$4,280.26    4.28%
357    \$3,438.36    3.44%
358    \$2,589.44    2.59%
359    \$1,733.45    1.73%
360     \$870.32     0.87%
Total     Actual    PV Total
Principal   Interest   Payment   Cashflow   Cashflow
-\$98,000
\$44.24     \$833.33    \$877.57   \$877.57    \$870.32
\$44.61     \$832.96    \$877.57   \$877.57    \$863.13
\$44.98     \$832.59    \$877.57   \$877.57    \$855.99
\$45.35     \$832.22    \$877.57   \$877.57    \$848.92
\$45.73     \$831.84    \$877.57   \$877.57    \$841.90
\$46.11     \$831.46    \$877.57   \$877.57    \$834.94
\$46.50     \$831.07    \$877.57   \$877.57    \$828.04
\$46.88     \$830.69    \$877.57   \$877.57    \$821.20
\$47.27     \$830.30    \$877.57   \$877.57    \$814.41
\$47.67     \$829.90    \$877.57   \$877.57    \$807.68
\$48.07     \$829.51    \$877.57   \$877.57    \$801.01
\$48.47     \$829.10    \$877.57   \$877.57    \$794.39
\$48.87     \$828.70    \$877.57   \$877.57    \$787.82
\$49.28     \$828.29    \$877.57   \$877.57    \$781.31
\$49.69     \$827.88    \$877.57   \$877.57    \$774.86
\$50.10     \$827.47    \$877.57   \$877.57    \$768.45
\$50.52     \$827.05    \$877.57   \$877.57    \$762.10
\$50.94     \$826.63    \$877.57   \$877.57    \$755.80
\$51.37     \$826.21    \$877.57   \$877.57    \$749.56
\$51.79     \$825.78    \$877.57   \$877.57    \$743.36
\$52.23     \$825.35    \$877.57   \$877.57    \$737.22
\$52.66     \$824.91    \$877.57   \$877.57    \$731.13
\$53.10     \$824.47    \$877.57   \$877.57    \$725.08
\$53.54     \$824.03    \$877.57   \$877.57    \$719.09
\$53.99     \$823.58    \$877.57   \$877.57    \$713.15
\$54.44     \$823.13    \$877.57   \$877.57    \$707.25
\$54.89     \$822.68    \$877.57   \$877.57    \$701.41
\$55.35     \$822.22    \$877.57   \$877.57    \$695.61
\$55.81     \$821.76    \$877.57   \$877.57    \$689.86
\$56.28     \$821.30    \$877.57   \$877.57    \$684.16
\$56.74     \$820.83    \$877.57   \$877.57    \$678.51
\$57.22     \$820.35    \$877.57   \$877.57    \$672.90
\$57.69     \$819.88    \$877.57   \$877.57    \$667.34
\$58.17     \$819.40    \$877.57   \$877.57    \$661.82
\$58.66     \$818.91    \$877.57   \$877.57    \$656.35
\$59.15     \$818.42    \$877.57   \$877.57    \$650.93
\$59.64   \$817.93   \$877.57   \$877.57   \$645.55
\$60.14   \$817.43   \$877.57   \$877.57   \$640.21
\$60.64   \$816.93   \$877.57   \$877.57   \$634.92
\$61.14   \$816.43   \$877.57   \$877.57   \$629.68
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\$807.68    \$69.89   \$877.57   \$877.57       \$47.67
\$814.41    \$63.16   \$877.57   \$877.57       \$47.27
\$821.20    \$56.37   \$877.57   \$877.57       \$46.88
\$828.04    \$49.53   \$877.57   \$877.57       \$46.50
\$834.94    \$42.63   \$877.57   \$877.57       \$46.11
\$841.90    \$35.67   \$877.57   \$877.57       \$45.73
\$848.92    \$28.65   \$877.57   \$877.57       \$45.35
\$855.99    \$21.58   \$877.57   \$877.57       \$44.98
\$863.13    \$14.45   \$877.57   \$877.57       \$44.61
\$870.32     \$7.25   \$877.57   \$877.57       \$44.24

\$315,925.77   \$100,000.00
PV
Servicing   Servicing

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\$0.00   \$0.00

\$0.00
FIXED RATE MORTGAGE: QUESTIONS

<< Unless otherwise directed assume that the service rate is zero. >>

1) What is the monthly payment on a 30 year, 9% mortgage on \$1,000,000?

2) In the above mortgage, which is the first period to have more of
the payment go to principal repayment than to interest repayment?
Do you see any correlation to this and the proportion outstanding?

3) Using a 30 year, 8% mortgage on \$100,000, what is the effective
yield or borrowing cost if there are 2 points on the mortgage?
What if there are 3 points? ...5 points?

4) Using the same mortgage as in #3, with 2 points, what happens
to the effective yield if the mortgage is prepaid after 20 years?
...10 years? ...5 years?

5) Using a 30 year, 10% mortgage on \$200,000 with no points and a
6% prepayment penalty, what is the effective yield if the loan is
held until maturity? ...if it is prepaid after 15 years? ...after
5 years?

6) How much interest is paid over the life of a 30 year, \$150,000
mortgage at 8% interest? How much is this as a percentage of the
original loan?

7) Using a 30 year, 6% mortgage on \$150,000, with 2 points and a 6%
prepayment penalty, what is the effective yield if the mortgage is
prepaid after 20 years? ...15 years? ...5 years?

8) Imagine that you are a portfolio manager for a small bank. You are
considering selling some of your newly originated loans into the
secondary market to generate new capital for the bank to lend.
The market discount rate for 30 year mortgages is 9%. Price the
following mortgages;
Initial                 Interest                Term
Principal                   Rate                 (Years)
-------------            -------------          -------------
Mortgage A               200,000                     9.00%                       30
Mortgage B               190,000                    11.00%                       30
Mortgage C               270,000                     5.50%                       30

9) You are now trying to value two mortgages, both have \$1,000,000
principal, with rates of 8.5% and 9%. You expect that the mortgages
are equally likely to prepay in year 7 or year 12. If the market
discount rate is 8%, what is the value of these two mortgages?

10)One of the chief sources of income for mortgage originators is
the servicing fee, which is retained even if the mortgage is sold.
The fee covers administrative duties such as accounting and
collection of monthly payment. It is stated as a percent of the
outstanding principal balance and is paid yearly out of the
interest cashflow. What is the value of a .5% servicing contract
on the mortgage in question #1?

End of Question Section
Servicing
FIXED RATE MORTGAGE: QUESTIONS

1. \$8,046.23 or .008046 of the initial principal.

2. This occurs in month number 274. The proportion outstanding is equal to approximately 1/2.

3. Points              Effective Yield
2             8.21%
3             8.32%
5            8.55%

4. Prepaid in year     Effective Yield
20           8.23%
10           8.31%
5            8.50%

5. Prepaid in year     Effective Yield
Never             10.00%
15             10.15%
5            10.89%

6. You would pay \$246,233 in interest or slightly over 160% of the original principal balance.

7. Prepaid in year     Effective Yield
20             6.30%
15             6.42%
5        7.45%

8. Mortgage            Price
A             \$200,000
B             \$224,877
C             \$190,528

9. Mortgage            7 yr value               12 yr value           Price
9.00%               \$1,052,118               \$1,073,376            \$1,062,747
8.50%               \$1,025,994               \$1,036,534            \$1,031,264

10. \$40,352
Servicing

```
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