Mortgages. Almost everyone who buys a home requires a loan from the bank. A mortgage is repaid over...
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Transcript of Mortgages. Almost everyone who buys a home requires a loan from the bank. A mortgage is repaid over...
![Page 1: Mortgages. Almost everyone who buys a home requires a loan from the bank. A mortgage is repaid over a set length of time, known as the amortization period.](https://reader036.fdocuments.net/reader036/viewer/2022062719/56649ef15503460f94c02d59/html5/thumbnails/1.jpg)
Mortgages
![Page 2: Mortgages. Almost everyone who buys a home requires a loan from the bank. A mortgage is repaid over a set length of time, known as the amortization period.](https://reader036.fdocuments.net/reader036/viewer/2022062719/56649ef15503460f94c02d59/html5/thumbnails/2.jpg)
Almost everyone who buys a home requires a loan from the bank.
• A mortgage is repaid over a set length of time, known as the amortization period.
• A mortgage is a loan specifically given for the purchase of a house.
![Page 3: Mortgages. Almost everyone who buys a home requires a loan from the bank. A mortgage is repaid over a set length of time, known as the amortization period.](https://reader036.fdocuments.net/reader036/viewer/2022062719/56649ef15503460f94c02d59/html5/thumbnails/3.jpg)
•During this period (could be up to 30 years), the conditions of the mortgage usually change (interest).
•Mortgage calculations are done using the present value of an annuity formula.
![Page 4: Mortgages. Almost everyone who buys a home requires a loan from the bank. A mortgage is repaid over a set length of time, known as the amortization period.](https://reader036.fdocuments.net/reader036/viewer/2022062719/56649ef15503460f94c02d59/html5/thumbnails/4.jpg)
In Canada, Mortgages must be compounded S-A (says the Feds), but most
people tend to make monthly payments.
• The discrepancy between compounding periods and payments periods must be addressed before any calculations can be made.
![Page 5: Mortgages. Almost everyone who buys a home requires a loan from the bank. A mortgage is repaid over a set length of time, known as the amortization period.](https://reader036.fdocuments.net/reader036/viewer/2022062719/56649ef15503460f94c02d59/html5/thumbnails/5.jpg)
Converting a S-A rate to a monthly rate:
• Suppose you can get a mortgage rate of 8%.
• Let the monthly interest rate be i.
• We will consider 2 ways of looking at the interest calculation.
![Page 6: Mortgages. Almost everyone who buys a home requires a loan from the bank. A mortgage is repaid over a set length of time, known as the amortization period.](https://reader036.fdocuments.net/reader036/viewer/2022062719/56649ef15503460f94c02d59/html5/thumbnails/6.jpg)
Option #1
Consider the interest on $1.00 (C:M) for 6 months.
$1.00(1 + i)6
= (1 + i)6
![Page 7: Mortgages. Almost everyone who buys a home requires a loan from the bank. A mortgage is repaid over a set length of time, known as the amortization period.](https://reader036.fdocuments.net/reader036/viewer/2022062719/56649ef15503460f94c02d59/html5/thumbnails/7.jpg)
Option #2
Consider the interest on $1.00
(C:S-A) for 6 months.
$1.00(1.04)1
= (1.04)1
![Page 8: Mortgages. Almost everyone who buys a home requires a loan from the bank. A mortgage is repaid over a set length of time, known as the amortization period.](https://reader036.fdocuments.net/reader036/viewer/2022062719/56649ef15503460f94c02d59/html5/thumbnails/8.jpg)
KEY
Since these 2 options must yield the same interest
Take the 6th root of each side
(1 + i)6 = (1.04)1
[(1 + i)6]1/6 = [(1.04)1]1/6
1 + i = 1.006 558 197 i = 1.006 558 197 - 1
i = 0.656%
![Page 9: Mortgages. Almost everyone who buys a home requires a loan from the bank. A mortgage is repaid over a set length of time, known as the amortization period.](https://reader036.fdocuments.net/reader036/viewer/2022062719/56649ef15503460f94c02d59/html5/thumbnails/9.jpg)
John gets approved for a mortgage of $100 000 at 8.5% for 25 years.
a) What are the monthly payments?
b) How much interest does John pay?
First, convert the interest:
i = 8.5% (C:S-A) = 8.5 / 2 = 0.0425
![Page 10: Mortgages. Almost everyone who buys a home requires a loan from the bank. A mortgage is repaid over a set length of time, known as the amortization period.](https://reader036.fdocuments.net/reader036/viewer/2022062719/56649ef15503460f94c02d59/html5/thumbnails/10.jpg)
(1 + i)6 = 1.0425
i = 0.696%
n = 12 months X 25 years = 300 cycles
Use the formula for present value:
For monthly payments, use the KEY
![Page 11: Mortgages. Almost everyone who buys a home requires a loan from the bank. A mortgage is repaid over a set length of time, known as the amortization period.](https://reader036.fdocuments.net/reader036/viewer/2022062719/56649ef15503460f94c02d59/html5/thumbnails/11.jpg)
PV = R[1 – (1 + i)-n]i
R = ?,
PV = 100 000
i = 0.00696
n = 300
100 000 = R[1 – (1 + 0.00696)-300]0.00696
R = $795.28
![Page 12: Mortgages. Almost everyone who buys a home requires a loan from the bank. A mortgage is repaid over a set length of time, known as the amortization period.](https://reader036.fdocuments.net/reader036/viewer/2022062719/56649ef15503460f94c02d59/html5/thumbnails/12.jpg)
How much interest was paid?
b) 300 payments of $795.28
John pays 300 X $795.28 = $238 583.42
Therefore: $238 583.42 - $100000 =
$138 583.42 in interest !!!!!He pays more in interest than the entire cost of the house…
![Page 13: Mortgages. Almost everyone who buys a home requires a loan from the bank. A mortgage is repaid over a set length of time, known as the amortization period.](https://reader036.fdocuments.net/reader036/viewer/2022062719/56649ef15503460f94c02d59/html5/thumbnails/13.jpg)