RE 611 / Fin 611 – Real Estate Finance
Lecture Notes – Fixed-rate Mortgages
1) Fixed-rate, Fully Amortizing Mortgages a) Constant Amortization Mortgages (CAM)
Following the Depression, the long expansion and growth in incomes made lenders recognize longer term loans might be feasible. One early type of amortizing mortgage was the CAM. Key features include Principal payments:
Interest charges:
Consider a $75,000, 7.75% interest, 30-year CAM with monthly payments. In the first month Principal payment due:
Accrued interest:
Total payment:
Ending balance:
In the second month Principal payment due:
Accrued interest:
Total payment:
Ending balance:
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Monthly amortization table for this CAM:
Monthly Amortization Table
Constant Amortization Mortgage Initial Loan Amount Interest Rate Term in Years Month 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Opening Balance $75,000.00 $74,791.67 $74,583.33 $74,375.00 $74,166.67 $73,958.33 $73,750.00 $73,541.67 $73,333.33 $73,125.00 $72,916.67 $72,708.33 $72,500.00 $72,291.67 $72,083.33 $71,875.00 $71,666.67 $71,458.33 $71,250.00 $71,041.67 $70,833.33 $70,625.00 $70,416.67 $70,208.33 $75,000.00 7.75% 30 Monthly Payment $692.71 $691.36 $690.02 $688.67 $687.33 $685.98 $684.64 $683.29 $681.94 $680.60 $679.25 $677.91 $676.56 $675.22 $673.87 $672.53 $671.18 $669.84 $668.49 $667.14 $665.80 $664.45 $663.11 $661.76 Interest $484.38 $483.03 $481.68 $480.34 $478.99 $477.65 $476.30 $474.96 $473.61 $472.27 $470.92 $469.57 $468.23 $466.88 $465.54 $464.19 $462.85 $461.50 $460.16 $458.81 $457.47 $456.12 $454.77 $453.43 Amortization $208.33 $208.33 $208.33 $208.33 $208.33 $208.33 $208.33 $208.33 $208.33 $208.33 $208.33 $208.33 $208.33 $208.33 $208.33 $208.33 $208.33 $208.33 $208.33 $208.33 $208.33 $208.33 $208.33 $208.33 Ending Balance $74,791.67 $74,583.33 $74,375.00 $74,166.67 $73,958.33 $73,750.00 $73,541.67 $73,333.33 $73,125.00 $72,916.67 $72,708.33 $72,500.00 $72,291.67 $72,083.33 $71,875.00 $71,666.67 $71,458.33 $71,250.00 $71,041.67 $70,833.33 $70,625.00 $70,416.67 $70,208.33 $70,000.00
Note that the payment drops each year. Because incomes typically rise, this structure puts a heavy burden on lower-income borrowers, who have difficulty in meeting the initial payments.
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b) Fully-amortizing, Constant-payment Mortgages (CPM)
These are the normal fixed-rate mortgages; unless otherwise specified, when we talk about fixed-rate mortgages we are talking about CPMs. Payment remains constant each month, but the amount of amortization does not. Instead, amortization changes each month based on the interest that accrues, with the payment structured so that the principal balance is fully repaid at the end of the loan’s term. These mortgages are simply annuities: PV = PMT PVIFA, where
1 1 PVIFA 1 . n (1 i ) i
Note that the interest rate in this expression is the periodic interest rate, and n is the number of periods. This implies that PMT = PV Mortgage Constant, where
MC i ,n 1 / PVIFA i (1 i ) n (1 i ) n 1
Think of the mortgage constant as:
Mortgage constants are calculated in the appendix; look under the column payment required to amortize $1. These tables used to be the easiest way to calculate mortgage payments, before financial calculators. Even now, the mortgage constant can be a useful construct for thinking of the “cost of debt.”
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What is the monthly payment on a $75,000, 30-year, fixed-rate, constantpayment mortgage at 7.75 percent interest with monthly payments?
How much of the payment in the first month is interest? How much is principal? What is the balance due at the end of the month?
Suppose that the first payment is on January 1st of this year. How much total interest will be paid on this loan during this year?
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Suppose instead that the first payment will be on March 1st. How much interest will be paid on the loan this year?
How much interest will be paid on this loan next year?
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Monthly amortization table for this fixed-rate, constant payment mortgage:
Monthly Amortization Table
Constant Payment Mortgage Initial Loan Amount Interest Rate Term in Years Month 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Opening Balance $75,000.00 $74,947.07 $74,893.79 $74,840.17 $74,786.20 $74,731.89 $74,677.22 $74,622.20 $74,566.83 $74,511.10 $74,455.01 $74,398.55 $74,341.73 $74,284.55 $74,226.99 $74,169.07 $74,110.77 $74,052.09 $73,993.03 $73,933.60 $73,873.77 $73,813.57 $73,752.97 $73,691.98 $75,000.00 7.75% 30 Monthly Payment $537.31 $537.31 $537.31 $537.31 $537.31 $537.31 $537.31 $537.31 $537.31 $537.31 $537.31 $537.31 $537.31 $537.31 $537.31 $537.31 $537.31 $537.31 $537.31 $537.31 $537.31 $537.31 $537.31 $537.31 Interest $484.38 $484.03 $483.69 $483.34 $482.99 $482.64 $482.29 $481.94 $481.58 $481.22 $480.86 $480.49 $480.12 $479.75 $479.38 $479.01 $478.63 $478.25 $477.87 $477.49 $477.10 $476.71 $476.32 $475.93 Amortization $52.93 $53.28 $53.62 $53.97 $54.31 $54.67 $55.02 $55.37 $55.73 $56.09 $56.45 $56.82 $57.19 $57.55 $57.93 $58.30 $58.68 $59.06 $59.44 $59.82 $60.21 $60.60 $60.99 $61.38 Ending Balance $74,947.07 $74,893.79 $74,840.17 $74,786.20 $74,731.89 $74,677.22 $74,622.20 $74,566.83 $74,511.10 $74,455.01 $74,398.55 $74,341.73 $74,284.55 $74,226.99 $74,169.07 $74,110.77 $74,052.09 $73,993.03 $73,933.60 $73,873.77 $73,813.57 $73,752.97 $73,691.98 $73,630.60
How much of the payment in the 60th month is interest? How much is principal? What is the balance due at the end of 60 months?
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c) Comparing IOs, CAMs and CPMs:
Fixed Rate Mortgage Payments
$800
Constant Payment Mortgage
$700 $600 $500 $400 $300 $200 $100 $0 1 2 3 4 5 6 7 8
Interest Only Mortgage Constant Amortization Mortgage
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Year
Comparing CAMs and CPMs $75,000, 30-year loans $600
$500
$400
$300
$200
CPM Interest CPM Amortization IO Interest CAM Interest CAM Amortization
$100
$0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Month
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