Unformatted text preview: Problem A5.4 ( Extra Credit). In this problem you will be asked to calculate the monthly payment of a mortgage. Suppose you borrow P dollars for M months at a rate r , starting in the ﬁrst day of Month 0. At the end of each month i , i = 0 , 1 ,...,M1, you pay q i , the interest for that month, which is P i · ( r/ 12), where P i is the balance at the beginning of Month i . You also pay p i dollars toward the principle, so that the balance of the principle becomes P i +1 = P ip i for the next month. In real life, your lender will “amortize” the payment so that p i + q i remains constant for all i , and you pay oﬀ your loan at the end of Month M1. Question: give close form expressions for p i and q i . 1...
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 Winter '07
 YaoyunShi
 University of Michigan

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