Chapter 14: The Mortgage Markets 81
11. Two mortgage options are available: a 15-year fixed-rate loan at 6% with no discount points, and a
15-year fixed-rate loan at 5.75% with 1 discount point. Assuming you will not pay off the loan early,
which alternative is best for you? Assume a $100,000 mortgage.
Solution: Determine the effective annual rate for each alternative.
12. Two mortgage options are available: a 30-year fixed-rate loan at 6% with no discount points, and a
30-year fixed-rate loan at 5.75% with one discount point. How long do you have to stay in the house
for the mortgage with points to be a better option? Assume a $100,000 mortgage.
Solution: The two loans have the same effective rate at the point of indifference.
13. Two mortgage options are available: a 30-year fixed-rate loan at 6% with no discount points, and
a 30-year fixed-rate loan at 5.75% with points. If you are planning on living in the house for 12 years,
what is the most you are willing to pay in points for the 5.75% mortgage? Assume a $100,000 mortgage.
Solution: 30-year fixed-rate loan at 6% with no discount points:
Chapter 14: The Mortgage Markets 83
The amortization table is:
Beginning
Balance
Payment
Interest
Principal
Ending
Balance
1
$250,000.00
$12,754.81
$15,000.00
($ 2,245.19)
$252,245.19
2
$252,245.19
$13,156.74
$15,134.71
($ 1,977.97)
$254,223.16
3
$254,223.16
$13,571.34
$15,253.39
($ 1,682.05)
$255,905.21
4
$255,905.21
$13,999.00
$15,354.31
($ 1,355.31)
$257,260.52
5
$257,260.52
$14,440.14
$15,435.63
($ 995.49)
$258,256.00
6
$258,256.00
$14,895.18
$15,495.36
($ 600.18)
$258,856.18
7
$258,856.18
$15,364.56
$15,531.37
($ 166.81)
$259,022.99
8
$259,022.99
$15,848.74
$15,541.38
$ 307.36
$258,715.63
9
$258,715.63
$16,348.16
$15,522.94
$ 825.23
$257,890.40
10
$257,890.40
$16,863.33
$15,473.42
$ 1,389.91
$256,500.50
11
$256,500.50
$17,394.73
$15,390.03
$ 2,004.70
$254,495.79
12
$254,495.79
$17,942.88
$15,269.75
$ 2,673.13
$251,822.66
13
$251,822.66
$18,508.30
$15,109.36
$ 3,398.94
$248,423.72
14
$248,423.72
$19,091.54
$14,905.42
$ 4,186.11
$244,237.61
15
$244,237.61
$19,693.15
$14,654.26
$ 5,038.90
$239,198.71
16
$239,198.71
$20,313.73
$14,351.92
$ 5,961.81
$233,236.90
17
$233,236.90
$20,953.86
$13,994.21
$ 6,959.65
$226,277.26
18
$226,277.26
$21,614.16
$13,576.64
$ 8,037.53
$218,239.73
19
$218,239.73
$22,295.27
$13,094.38
$ 9,200.89
$209,038.84
20
$209,038.84
$22,997.85
$12,542.33
$10,455.52
$198,583.32
21
$198,583.32
$23,722.56
$11,915.00
$11,807.56
$186,775.76
22
$186,775.76
$24,470.11
$11,206.55
$13,263.56
$173,512.20
23
$173,512.20
$25,241.22
$10,410.73
$14,830.49
$158,681.72
24
$158,681.72
$26,036.62
$ 9,520.90
$16,515.72
$142,165.99
25
$142,165.99
$26,857.10
$ 8,529.96
$18,327.14
$123,838.86
26
$123,838.86
$27,703.42
$ 7,430.33
$20,273.09
$103,565.77
27
$103,565.77
$28,576.42
$ 6,213.95
$22,362.47
$ 81,203.29
28
$ 81,203.29
$29,476.93
$ 4,872.20
$24,604.73
$ 56,598.87
29
$ 56,598.57
$30,405.81
$ 3,395.91
$27,009.89
$ 29,588.67
30
$ 29,588.67
$31,363.96
$ 1,775.32
$29,588.64
$ 0.00
17. Consider a growing equity mortgage on a $250,000 mortgage with yearly payments. The stated
interest rate on the mortgage is 6%, but this only applies to the 1st annual payment. Thereafter, the
annual payment will grow by 5.5797%. Develop an amortization table for this loan.
Solution: The payment for the 1st year is calculated as:
I = 6; PV = $250,000; FV = 0; N = 30
84 Mishkin/Eakins • Financial Markets and Institutions, Eighth Edition
The amortization table is:
Payment
Interest
Principal
Ending
Balance
1
$18,162.23
$15,000.00
$ 3,162.23
$246,837.77
2
$19,175.63
$14,810.27
$ 4,365.36
$242,472.41
3
$20,245.57
$14,548.34
$ 5,697.22
$236,775.19
4
$21,375.21
$14,206.51
$ 7,168.70
$229,606.49
5
$22,567.88
$13,776.39
$ 8,791.49
$220,815.00
6
$23,827.10
$13,248.90
$10,578.20
$210,236.79
7
$25,156.58
$12,614.21
$12,542.38
$197,694.42
8
$26,560.25
$11,861.67
$14,698.58
$182,995.84
9
$28,042.23
$10,979.75
$17,062.48
$165,933.36
10
$29,606.90
$ 9,956.00
$19,650.90
$146,282.46
11
431,258.88
$ 8,776.95
$22,481.93
$123,800.53
12
$33,003.03
$ 7,428.03
$25,575.00
$ 98,225.54
13
$34,844.50
$ 5,893.53
$28,950.96
$ 69,274.57
14
$36,788.72
$ 4,156.47
$32,632.24
$ 36,642.33
15
$38,841.42
$ 2,198.54
$36,642.88
$ 0.00
18. Rusty Nail owns his house free and clear, and it’s worth $400,000. To finance his retirement, he
acquires a reverse annuity mortgage (RAM) from his bank. The RAM provides a fixed monthly
payment over 15 years on 70% of the value of his home at 5%. The payments are made at the
beginning of the month. How much does Rusty get each month?
19. You are working with a pool of 1,000 mortgages. Each mortgage is for $100,000 and has a stated
annual interest rate (nominal) of 6.00%. The mortgages are all 30-year fixed rate fully amortizing.
Mortgage servicing fees are currently 0.25% annually. Complete the following table:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
Month
Beginning
Balance
Required
Payment
Interest
Principal
Expected
Prepayment
Servicing
Fees
Ending
Balance
1
100,000,000
500,000
99,551
16,665
2
33,322
99,750,430
Chapter 14: The Mortgage Markets 85
Solution:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
Month
Beginning
Balance
Required
Payment
Interest
Principal
Expected
Prepayment
Servicing
Fees
Ending
Balance
1
100,000,000
599,551
500,000
99,551
16,665
20,833
99,883,784
2
99,883,784
599,451
499,419
100,032
33,322
20,809
99,750,430
For month 1:
The required payment is:
PV = 100,000,000; I = 6/12; N = 360; FV = 0;
For month 2:
The required payment is:
Servicing Fees are:
0.0025/12 99,883,784 = 20,809