Question: When a debt is refinanced, sometimes the term of the loan (that is, the time it takes to repay the debt) is shortened. Suppose the

When a debt is refinanced, sometimes the term of the loan (that is, the time it takes to repay the debt) is shortened. Suppose the current interest rate is 7%, and a couple's current debt is $100,000. The monthly payment R of the refinanced debt is a function of the term of the loan, t, in years. If we represent this function by R = f (t), then the following table defines the function.

1980.12 15 5 898.83 10 1161.09 20 775.30 706.78 1028.39 25 12

(a) If they refinance for 20 years, what is the monthly payment? Write this correspondence in the form R = f (t).
(b) Find f(10) and write a sentence that explains its meaning.
(c) Is f (5 + 5) = f (5) + f (5)? Explain.

1980.12 15 5 898.83 10 1161.09 20 775.30 706.78 1028.39 25 12

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