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# The monthly payment that amortizes a loan of A dollars in t years when the interest rate is r/year compounded monthly, is given by $P=f(A, r, t)=\frac{A r}{12\left[1-\left(1+\frac{r}{12}\right)^{-12 t}\right]}$ a. What is the monthly payment for a home mortgage of $300,000 that will be amortized over 30 years with an interest rate of 4%/year? An interest rate of 6%/year? b. Find the monthly payment for a home mortgage of$300,000 that will be amortized over 20 years with an interest rate of 6%/year.

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(a)

We are looking for

$f(300000, 0.04, 30)=\frac {300000\cdot 0.04 } {12\left[ 1-\left( 1+\frac { 0.04} {12 } \right)^{ -360 } \right] }= \boxed {1432.25} \quad \text {(in dollars) }$

and

$f(300000, 0.06, 30)=\frac {300000\cdot 0.06 } {12\left[ 1-\left( 1+\frac { 0.06} {12 } \right)^{ -360 } \right] }=\boxed {1798.65} \quad \text {(in dollars) }$

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