# financal market and institution chapter 14

Chapter 14

Questions

1.Securities in the mortgage markets are collateralized by real estate. 6.The down payment means that if the borrower chooses not make payments on the loan, the borrower will suffer some financial loss. This increases the likelihood that the borrower will continue to make the promised payments. 7.Lenders may require private mortgage insurance.

13.The bank accepts the home as security and advances money each month. When the borrower dies, the borrower’s estate sells the property to retire the debt. Quantitative Problems

1.Compute the required monthly payment on a $80,000 30-year, fixed-rate mortgage with a nominal interest rate of 5.80%. How much of the payment goes toward principal and interest during the first year? Solution:The monthly mortgage payment is computed as:

N 360; I 5.8/12; PV 80,000; FV 0

Compute PMT; PMT $469.4024

The amortization schedule is as follows:

Month BeginningBalance Payment InterestPaid PrincipalPaid EndingBalance 1 $80,000.00 $ 469.40 $ 386.67 $ 82.74 $79,917.26

2 $79,917.26 $ 469.40 $ 386.27 $ 83.14 $79,834.13

3 $79,834.13 $ 469.40 $ 385.86 $ 83.54 $79,750.59

4 $79,750.59 $ 469.40 $ 385.46 $ 83.94 $79,666.65

5 $79,666.65 $ 469.40 $ 385.06 $ 84.35 $79,582.30

6 $79,582.30 $ 469.40 $ 384.65 $ 84.75 $79,497.55

7 $79,497.55 $ 469.40 $ 384.24 $ 85.16 $79,412.38

8 $79,412.38 $ 469.40 $ 383.83 $ 85.58 $79,326.81

9 $79,326.81 $ 469.40 $ 383.41 $ 85.99 $79,240.82

10 $79,240.82 $ 469.40 $ 383.00 $ 86.41 $79,154.41

11 $79,154.41 $ 469.40 $ 382.58 $ 86.82 $79,067.59

12 $79,067.59 $ 469.40 $ 382.16 $ 87.24 $78,980.35

Total $5,632.83 $4,613.18 $1,019.65 Alternatively: cumulative interest paid over a period of time is the total payment subtracting the principal paid. The total payments = 469.4024 x 12 = $5,632.83. The ending balance after 12 payments can be found with a financial calculator: N 12; I 5.8/12; PV 80,000; PMT $469.4024; FV ? Compute FV; FV $78,980.35

The total principal paid = the mortgage amount minus the ending balance at t=12 = 80,000 – 78,980.35 = 1,019.65. Therefore, the total interest paid in the first year = 5,632.83 – 1,019.65 = 4,613.18 2.Compute the face value of a 30-year, fixed-rate mortgage with a monthly payment of $1,100, assuming a nominal interest rate of 9%. If the mortgage requires 5% down, what is the maximum house price? Solution:The PV of the payments is:

N 360; I 9/12; PV 1100; FV 0

Compute PV; PV 136,710

The maximum house price is 136,710/0.95 $143,905

3.Consider a 30-year, fixed-rate mortgage for $100,000 at a nominal rate of 9%. If the borrower wants to pay off the remaining balance on the mortgage after making the 12th payment, what is the remaining balance on the mortgage? Solution:The monthly mortgage payment is computed as:

N 360; I 9/12; PV 100,000; FV 0

Compute PMT; PMT $804.62

To find out how much is owed at the end of 12 payments:

N 12; I 9/12; PV -100,000; PMT $804.62

Compute FV; FV $99,316.80

OR

N 360-12; I 9/12; PV ?; PMT -$804.62; FV 0 Compute PV; PV $99,316.80

Just after making the 12th payment, the borrower must pay $99,316.80 to pay off the loan. 4.Consider a 30-year, fixed-rate mortgage for $100,000 at a nominal rate of 9%. If the borrower pays an additional $100 with each payment, how fast will the mortgage be paid off? Solution:The monthly mortgage payment is computed as:

N 360; I 9/12; PV 100,000; FV 0

Compute PMT; PMT $804.62

The borrower is sending in $904.62 each month. To determine when the loan will be retired: PMT 904.62; I 9/12; PV 100,000; FV 0

Compute N; N 237, or after 19.75 years.

8.A 30-year, variable-rate mortgage offers a first-year teaser rate of 2%. After that, the rate starts at 4.5%, adjusted based on actual interest states. The maximum rate over the life of the...

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