(d) Include prepayment penalty of 2% of $83,186.41 or $1,663.73
Solution i:
Problem 4-15
Points required to achieve a yield to 10% for the 25 year loan. Fv is now $83,186.41 = $1,663.73 = $84,850.14
Monthly payments PMT (n,i,PV,FV):
n = 300
i = 9% 12
Problem 4-16
(a) In order to find which loan is the better choice after 20 years, the effective interest rate for each loan must be calculated.
Loan A
Loan B
Principal
$75,000
$75,000
Nominal interest rate
6.00%
7.00%
Term (years)
30
30
Points
6
2
Payment
$449.66
$498.98
Loan Balance after 20 years
$40,502.43
$42,975.33
Loan Balance after 5 years
$69,790.32
$70,599.14
Loan A
Loan B
Loan A
i = .623917% * 12 = 7.49%
Loan B
The borrower would be indifferent between the two loans if the repayment period is 5 years.
Problem 4-17
(a) Monthly Payments = $1,382.50 to be made to the borrower
Note: Balance at the end
Note: Balance at the end
of 60 months = $70,599.14
Problem 4-18
Find the balance at the end of 5 years for a fully amortizing $200,000, 10% mortgage with a 25 year amortization schedule:
PV = -200,000 FV = 0
Problem 4- 19
CAM loan:
(a) Calculate constant monthly amortization:
$125,000 240 months = $520.83 per month
Calculate Monthly Interest:
Month
Rate
Interest
Amortization
Total Payment
End Balance
1
*11%/12
1,145.83
520.83
1,666.66
124,479.17
2
*11%/12
1,141.05
520.83
1,661.88
123,958.34
3
*11%/12
1,136.28
520.83
1,657.11
123,437.51
4
*11%/12
1,131.51
520.83
1,652.34
122,916.68
5
*11%/12
1,126.74
520.83
1,647.57
122,395.85
6
*11%/12
1,121.96
520.83
1,642.79
121,875.02
(b) For a constant payment loan (CPM) we have:
PV = -$125,000
n = 240
i = 11% 12
FV = 0
Solve PMT = $1,290.24
(c) In the absence of point and origination fees, the effective interest rates on both loans will be an annual rate of 11%, compounded
monthly. This is true regardless of when either of the loans are repaid. Monthly payments are different, however i is the same for
both loans.
Problem 4-20
(a) Determine monthly payments based on interest being accrued daily.
Solve for interest due at the end of month one:
Problem 4- 21 Comprehensive Review Problem
(1) Fully amortizing:
(2) Partial amortizing:
(3) Interest only
(4) Negative amortization:
PV = -100,000 n = 240
i = 12% Solve PMTs = $949.46
FV = 150,000
B. Loan Balances for A.1. – A.4 after 5 years
n = 180
C. Interest at the end of month 61 for A.1 – A.4
D. APR* for loans in A.1 – A.4
E. Effective yield if loan prepaid EOY5. Balances must be calculated at EOY5 for each loan (not shown).
F. “Interest only” monthly payments in A.1 = $100,000 * (12% 12) or $1,000 per month for 36 mos. What must
payments be from yr. 4-17 to fully amortize the loan at the end of 240 mos.?
(2) n = 204 FV = 150,000
(3) 12% because there are no points
(4) 4 points charged, loan payoff 36 months, what is effective interest rate?
Problem 4-22
Problem 4-23
Chapter 4 Appendix
Questions
Question 4-A1
Why do monthly mortgage payments increase so sharply during periods of inflation? What does the tilt effect have to do with
this?
Question 4-A2
As inflation increases, the impact of the tilt effect is said to become even more burdensome on borrowers. Why is this so?
Problem 4A-1
(a) Year Payment
CFj = 498.57
nj = 12
CFj = 576.16
nj = 12
CFj = 665.82
nj = 12
CFj = 715.76
nj = 11*
Problem 4A-2
Excel template Ch4 GPM from course website modified to solve this problem.
Chapter 4
Loan Balance on GPM
Spreadsheet Limitations: Projections for 5 years
Input Assumptions
Loan Amount
$100,000
Interest Rate
9.00%
Loan Term
25
years
Pmt Increase
7.50%
Inc. Years
3
Points
4
Lender’s Yield (after 7 yrs)
10.02%
INITIAL PAYMENT CALCULATION:
(1)
(2)
(3)
(4)
(5)
Payment
Period
Payment
MPVIFA
MPVIF
(2x3x4)
1
1.00000
11.43491
1.00000
11.43491
2
1.07500
11.43491
0.91424
11.23830
3
1.15563
11.43491
0.83583
11.04507
4
1.24230
11.43491
0.76415
10.85516
5
1.24230
11.43491
0.69861
9.92420
6-25
1.24230
111.14495
0.63870
88.18848
Pmt factor =
142.68613
Initial Payment:
$700.84
<====
$100,000
142.68613
Loan Amt
/ Pmt Factor
a. Calculation of initial payment is shown above. Payments for years 2 through 5 are shown in the exhibit below.
b. The loan balance at the end of year 3 is shown in the exhibit below.
36 $809.91 $750.00 $59.91 $99,940 $839.20 EOY 3
Month Payment Interest Principle Balance
CPM Payment
0 ($96,000) <==Amount Dispersed $100,000
1$700.84 $750.00 ($49.16) $100,049 $839.20
2$700.84 $750.37 ($49.53) $100,099 $839.20
3$700.84 $750.74 ($49.90) $100,149 $839.20
4$700.84 $751.11 ($50.28) $100,199 $839.20
5$700.84 $751.49 ($50.65) $100,250 $839.20
6$700.84 $751.87 ($51.03) $100,301 $839.20
7$700.84 $752.25 ($51.42) $100,352 $839.20
9$700.84 $753.03 ($52.19) $100,456 $839.20
11 $700.84 $753.81 ($52.98) $100,562 $839.20
13 $753.40 $754.61 ($1.21) $100,616 $839.20
15 $753.40 $754.63 ($1.23) $100,619 $839.20
16 $753.40 $754.64 ($1.24) $100,620 $839.20
17 $753.40 $754.65 ($1.25) $100,621 $839.20
18 $753.40 $754.66 ($1.26) $100,622 $839.20
19 $753.40 $754.67 ($1.27) $100,624 $839.20
23 $753.40 $754.71 ($1.30) $100,629 $839.20
29 $809.91 $753.05 $56.86 $100,350 $839.20
30 $809.91 $752.62 $57.28 $100,293 $839.20
31 $809.91 $752.19 $57.71 $100,235 $839.20
32 $809.91 $751.76 $58.14 $100,177 $839.20
33 $809.91 $751.33 $58.58 $100,118 $839.20
34 $809.91 $750.89 $59.02 $100,059 $839.20
LOAN AMORTIZATION SCHEDULE:
c.
Input Assumptions
Loan Amount
$100,000
Interest Rate
9.00%
Loan Term
25
years
Pmt Increase
7.50%
Inc. Years
3
Points
4
Lender’s Yield (after 7 yrs)
10.02%
Problem 4A-3
The initial payment would now be $518.09 as shown below.
Chapter 4
Loan Balance on GPM
Spreadsheet Limitations: Projections for 7 years
Input Assumptions
Loan Amount
$60,000
Interest Rate
12.00%
Loan Term
30
years
Pmt Increase
5.00%
Inc. Years
5
Points
0
Lender’s Yield (after 7 yrs)
12.00%
INITIAL PAYMENT CALCULATION:
(1)
(2)
(3)
(4)
(5)
Payment
Period
Payment
MPVIFA
MPVIF
(2x3x4)
1
1.00000
11.25508
1.00000
11.25508
2
1.05000
11.25508
0.88745
10.48773
3
1.10250
11.25508
0.78757
9.77269
4
1.15763
11.25508
0.69892
9.10640
5
1.21551
11.25508
0.62026
8.48555
6-25
1.27628
94.94655
0.55045
66.70268
Pmt factor =
115.81012
Initial Payment:
$518.09
<====
$60,000
115.81012
Loan Amt
/ Pmt Factor