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Unformatted text preview: 1 Equity and Interest Payments on a Loan Previous Example: Home Mortgage Price of home: $220,000 Down payment: $20,000 Loan (home mortgage): $220,000  $20,000 = $200,000 Duration of loan: 15 years = 180 months Interest rate: 7.2% per year, compounded monthly Payment frequency: monthly 1 2 A A A A 179 180 months P = $200,0000 IOE 201 Lecture Notes 7 2  + + = 1 ) 1 ( ) 1 ( N N i i i P A Monthly payment Loan (home mortgage) P = $200,000 Duration of loan N = 180 months Interest rate i = 7.2% per year = 0.072/12 = 0.006 per month  + + = 1 ) 006 . 1 ( ) 006 . 1 ( 006 . 000 , 200 $ 180 180 = $1,820 Of this $1,820 per month, a portion is paid against the principal ( equity payment ), and a portion is paid against the interest ( interest payment ). The two portions vary with each months payment. The sum of the two portions is the total monthly payment ($1,820) Equity and Interest Payments on a Loan 3 Equity and Interest Payments on a Loan Loan (home mortgage) P = $200,000 for 15 years Interest rate i = 0.006 per month Monthly payment A = $1,820 Month 1: Interest on the principal at the end of 1 st month is $200,000 0.006 = $1,200 Therefore, out of 1 st payment of $1,820 : Interest payment = $1,200 , and Payment against principal = $1,820  $1,200 = $620 Month 2: Unpaid principal left after 1 st payment is $200,000  $620 = $199,380 Interest on unpaid principal at the end of the 2 nd month is $199,380 0.006 = $1,196.28 Interest payment = $1,196.28 , and Payment against principal = $1,820  $1,196.28 = $623.72 4 Equity and Interest Payments on a Loan Loan (home mortgage) P = $200,000 for 15 years Interest rate i = 0.006 per month Monthly payment A = $1,820 Month 3: Unpaid principal left after 2 nd payment is $199,380  $623.72 = $198,756.28 Interest on unpaid principal at the end of 3 rd month is $198,756.28 0.006 = $1,192.54 Interest payment = $1,192.54, and Payment against principal = $1,820  $1,192.54 = $627.46 With each subsequent months payment of $1,820: interest payment goes down...
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 Fall '09
 DennisBlumenfield

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