on october 1, the home mortgage balance was $282,000 for the home owned by patricia evans. the interest rate…

on october 1, the home mortgage balance was $282,000 for the home owned by patricia evans. the interest rate for the loan is 9 percent. assuming that patricia makes the october monthly mortgage payment of $2256, calculate the following: (a) the amount of interest included in the october payment (round your answer to the nearest cent). (b) the amount of the monthly mortgage payment that will be used to reduce the principal balance. (c) the new balance after patricia makes this monthly mortgage payment. (a) interest amount: $ (b) principal reduction: $ (c) new balance: $
Answer
Explanation:
Step1: Calculate monthly interest rate
The annual interest rate is 9% or 0.09. The monthly interest rate $r$ is $\frac{0.09}{12}= 0.0075$.
Step2: Calculate interest amount in October payment
The mortgage balance is $P = 282000$. The interest amount $I$ in the October payment is $I=P\times r=282000\times0.0075 = 2115$.
Step3: Calculate principal - reduction amount
The monthly mortgage payment is $M = 2256$. The principal - reduction amount $PR$ is $PR = M - I=2256 - 2115=141$.
Step4: Calculate new balance
The new balance $NB$ is $NB=P - PR=282000 - 141 = 281859$.
Answer:
(a) $$2115.00$ (b) $$141.00$ (c) $$281859.00$