the potters want to buy a small cottage costing $132,000 with annual insurance and taxes of $700 and $2900…

Explanation:

Step1: Calculate the loan amount

The cost of the cottage is $132000$ and the down - payment is $8000$. So the loan amount $P$ is $132000 - 8000=124000$.

Step2: Determine the monthly interest rate and number of payments

The annual interest rate $r = 6%=0.06$, so the monthly interest rate $i=\frac{0.06}{12}=0.005$. The loan term is $n = 20$ years, and the number of monthly payments $m=20\times12 = 240$.

Step3: Calculate the monthly mortgage payment

We use the formula for the monthly payment of a fixed - rate mortgage $M=\frac{P\times i\times(1 + i)^m}{(1 + i)^m-1}$. Substitute $P = 124000$, $i = 0.005$ and $m = 240$ into the formula: [ \begin{align*} M&=\frac{124000\times0.005\times(1 + 0.005)^{240}}{(1+0.005)^{240}-1}\ &=\frac{620\times(1.005)^{240}}{(1.005)^{240}-1} \end{align*} ] Using a calculator, $(1.005)^{240}\approx3.310204$. Then $M=\frac{620\times3.310204}{3.310204 - 1}=\frac{2052.32648}{2.310204}\approx888.37$.

Step4: Calculate the monthly insurance and tax payments

The annual insurance is $700$ and the annual tax is $2900$. The total annual cost for insurance and tax is $700 + 2900=3600$. The monthly cost for insurance and tax is $\frac{3600}{12}=300$.

Step5: Calculate the total monthly payment

The total monthly payment $T$ is the sum of the monthly mortgage payment and the monthly insurance and tax payment. So $T=888.37+300 = 1188.37$.

Answer:

A. No, because the total monthly payment is $$1188.37$