you can afford a $850 per month mortgage payment. youve found a 30 year loan at 7% interest.\na) how big of…

Explanation:

Step1: Calculate the monthly interest rate and number of payments

The annual interest rate ( r = 7%=0.07 ), so the monthly interest rate ( i=\frac{0.07}{12} ). The loan term is ( n = 30) years, and the number of monthly payments ( m=30\times12 = 360)

Step2: Use the present - value of an ordinary annuity formula for part (a)

The formula for the present value of an ordinary annuity is ( PV = PMT\times\frac{1-(1 + i)^{-m}}{i}), where (PMT=$850) [ \begin{align*} PV&=850\times\frac{1-(1+\frac{0.07}{12})^{-360}}{\frac{0.07}{12}}\ \end{align*} ] Let (x=(1+\frac{0.07}{12})^{-360}\approx0.1269) [ \begin{align*} PV&=850\times\frac{1 - 0.1269}{\frac{0.07}{12}}\ &=850\times\frac{0.8731}{\frac{0.07}{12}}\ &=850\times\frac{0.8731\times12}{0.07}\ &=850\times\frac{10.4772}{0.07}\ &=850\times149.6743\ &\approx127223.16 \end{align*} ]

Step3: Calculate the total amount paid for part (b)

The total amount paid (A = PMT\times m) Since (PMT = 850) and (m = 360) (A=850\times360=$306000)

Step4: Calculate the interest for part (c)

The interest (I=A - PV) We know (A = 306000) and (PV\approx127223.16) (I=306000- 127223.16=$178776.84)

Answer:

a) ($127223.16) b) ($306000) c) ($178776.84)