question\nthe price of a home is $300,000. after a 10% down payment, the mortgage is $270,000. if this is…

question\nthe price of a home is $300,000. after a 10% down payment, the mortgage is $270,000. if this is financed with a 30 - year fixed - rate mortgage at 6%, what is the monthly payment, excluding escrow taxes and insurance?\nround your answer to the nearest cent.\ndo not round until you have calculated the final answer.\nprovide your answer below:

question\nthe price of a home is $300,000. after a 10% down payment, the mortgage is $270,000. if this is financed with a 30 - year fixed - rate mortgage at 6%, what is the monthly payment, excluding escrow taxes and insurance?\nround your answer to the nearest cent.\ndo not round until you have calculated the final answer.\nprovide your answer below:

Answer

Explanation:

Step1: Identify the formula for monthly payment

The formula for the monthly payment ( M ) of a loan is ( M=\frac{P\times r\times(1 + r)^{n}}{(1 + r)^{n}-1} ), where ( P ) is the principal amount, ( r ) is the monthly interest rate, and ( n ) is the total number of payments.

Step2: Calculate ( r ) and ( n )

Given ( P = 270000 ), the annual interest rate ( i=6%=0.06 ). So the monthly interest rate ( r=\frac{0.06}{12}=0.005 ). The loan term is 30 years, so the total number of payments ( n = 30\times12=360 ).

Step3: Substitute values into the formula

Substitute ( P = 270000 ), ( r = 0.005 ), and ( n = 360 ) into the formula: [ \begin{align*} M&=\frac{270000\times0.005\times(1 + 0.005)^{360}}{(1+ 0.005)^{360}-1}\ \end{align*} ] First, calculate ( (1 + 0.005)^{360}). Using the formula ( a^{b}), where ( a = 1.005) and ( b = 360), ( (1.005)^{360}\approx6.022575 ). Then, ( 270000\times0.005=1350 ). The numerator is ( 1350\times6.022575 = 8129.47625 ). The denominator is ( 6.022575-1=5.022575 ). So ( M=\frac{8129.47625}{5.022575}\approx1618.56 ).

Answer:

( 1618.56 )