Math Problem Statement
our years ago Benencorp decided to expand its production capacity and borrowed $ 1.3 million for 20 years at 5.2 % compounded quarterly. After making 16 quarterly payments of $ 26,235.37 , Benencorp is considering refinancing this loan for 15 years at 4.8 % compounded quarterly, with refinancing charges of $ 5000 added to the amount of the new (refinanced) loan.
(a) Find the payoff amount of Benencorp’s original loan.
(b) Find the amount of the new loan and the new quarterly payment.
(c) Should Benencorp refinance?
Solution
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Math Problem Analysis
Mathematical Concepts
Loan Amortization
Compound Interest
Refinancing
Formulas
Loan balance formula for compounded interest: B = P(1 + i)^n - PMT * ((1 + i)^n - 1) / i
New loan balance with refinancing charges: New Loan = Payoff Amount + Refinancing Charges
Quarterly payment formula: PMT = (P * i) / [1 - (1 + i)^(-n)]
Theorems
Amortization Theorem
Compound Interest Theorem
Suitable Grade Level
Undergraduate Finance/Mathematics
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