you want to buy a $195,000 home. you plan to pay 20% as a down payment, and take out a 30 - year loan at…

Explanation:

Step1: Calculate loan amount

The home price is $195000$ and the down - payment is $20%$. So the loan amount $L$ is $(1 - 0.20)\times195000=0.8\times195000 = 156000$.

Step2: Calculate monthly interest rate and number of payments

The annual interest rate $r = 3.25%=0.0325$. The monthly interest rate $i=\frac{0.0325}{12}$. The number of payments $n = 30\times12=360$. We use the formula for the monthly payment of a loan $M=\frac{L\times i\times(1 + i)^n}{(1 + i)^n-1}$. Substitute $L = 156000$, $i=\frac{0.0325}{12}\approx0.00270833$, and $n = 360$ into the formula: [ \begin{align*} M&=\frac{156000\times0.00270833\times(1 + 0.00270833)^{360}}{(1+ 0.00270833)^{360}-1}\ \end{align*} ] $(1 + 0.00270833)^{360}\approx2.6179$. [ \begin{align*} M&=\frac{156000\times0.00270833\times2.6179}{2.6179 - 1}\ &=\frac{156000\times0.00270833\times2.6179}{1.6179}\ &=\frac{156000\times0.007083}{1.6179}\ &=\frac{1094.948}{1.6179}\ &\approx676.74 \end{align*} ]

Step3: Calculate first - payment interest

The first - payment interest is calculated based on the initial loan amount. The monthly interest rate $i=\frac{0.0325}{12}$. The initial loan amount $L = 156000$. The interest for the first month $I = L\times i=156000\times\frac{0.0325}{12}=422.5$.

Answer:

a) $156000$ b) $$676.74$ c) $422.50$