Math Problem Statement
Dave takes out a 26-year mortgage of 270000 dollars for his new house. Dave gets an interest rate of 15.6 percent compounded monthly. He agrees to make equal monthly payments, the first coming in one month. After making the 66th payment, Dave wants to buy a boat, so he wants to refinance his house to reduce his monthly payment by 400 dollars, and to get a better interest rate. In particular, he negotiates a new rate of 8.4 percent compounded monthly, and agrees to make equal monthly payments (each 400 dollars less than his original payments) for as long as necessary, followed by a single smaller payment. How large will Dave's final loan payment be?
Solution
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Math Problem Analysis
Mathematical Concepts
Loan Amortization
Compounded Interest
Refinancing
Algebra
Formulas
Monthly payment formula: M = P * (r(1 + r)^n) / ((1 + r)^n - 1)
Remaining balance formula: B = P * ((1 + r)^n - (1 + r)^k) / ((1 + r)^n - 1)
Refinanced loan formula: B = M_new * ((1 + r_new)^m - 1) / (r_new(1 + r_new)^m)
Theorems
Loan Amortization Theorem
Time Value of Money
Suitable Grade Level
College level or advanced high school (Grades 11-12)
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